Should I baptize my child myself?

No, you should not baptize your own child, unless you are duly ordained. The Westminster Confession of Faith Chapter 27.4 says:

There be only two sacraments ordained by Christ our Lord in the Gospel; that is to say, baptism, and the Supper of the Lord: neither of which may be dispensed by any, but by a minister of the Word lawfully ordained.

The Sacraments are official ordinances of the church commanded by Christ. In 1 Corinthians 4:1 the Apostle Paul says, "Let a man so account of us, as the ministers of Christ, and stewards of the mysteries of God." So, this particular work of ministry (Eph. 4:12) is not something that a unordained person should do, but is rather bestowed upon elders/ministers according to God's revealed will (Heb. 5:4).

As an example for instructions and how a minister should proceed, below is a related excerpt from the Book of Church Order of the Presbyterian Church in America.

Book of Church Order
CHAPTER 56

The Administration of Baptism

The Baptism of Infants and Children

56-1. Baptism is not to be unnecessarily delayed; not to be administered, in any case, by any private person; but by a minister of Christ, called to be the steward of the mysteries of God.

56-2. It is not to be privately administered, but in the presence of the congregation under the supervision of the Session.

56-3. After previous notice is given to the minister, the child to be baptized is to be presented, by one or both the parents, or some other responsible person, signifying the desire that the child be baptized.

56-4. Before baptism, the minister is to use some words of instruction, touching the institution, nature, use, and ends of this sacrament, showing:

a. That it is instituted by our Lord Jesus Christ;

b. That it is a seal of the Covenant of Grace, of our ingrafting into Christ, and of our union with Him, of remission of sins, regeneration, adoption, and life eternal;

c. That the water, in baptism, represents and signifies both the blood of Christ, which taketh away all guilt of sin, original and actual; and the sanctifying virtue of the Spirit of Christ against the dominion of sin, and the corruption of our sinful nature;

d. That baptizing, or sprinkling and washing with water, signifies the cleansing from sin by the blood and for the merit of Christ, together with the mortification of sin, and rising from sin to newness of life, by virtue of the death and resurrection of Christ;

e. That the promise is made to believers and their children; and that the children of believers have an interest in the covenant, and right to the seal of it, and to the outward privileges of the Church, under the Gospel, no less than the children of Abraham in the time of the Old Testament; the Covenant of Grace, for substance, being the same; and the grace of God, and the consolation of believers, more plentiful than before;

f. That the Son of God admitted little children into His presence, embracing and blessing them, saying, "For of such is the kingdom of God";

g. That children by Baptism, are solemnly received into the bosom of the Visible Church, distinguished from the world, and them that are without, and united with believers; and that all who are baptized in the name of Christ, do renounce, and by their Baptism are bound to fight against the devil, the world, and the flesh;

h. That they are federally holy before Baptism, and therefore are they baptized;

i. That the inward grace and virtue of Baptism is not tied to that very moment of time wherein it is administered; and that the fruit and power thereof reaches to the whole course of our life; and that outward baptism is not so necessary, that through the want thereof, the infant is in danger of damnation;

j. By virtue of being children of believing parents they are, because of God's covenant ordinance, made members of the Church, but this is not sufficient to make them continue members of the Church. When they have reached the age of discretion, they become subject to obligations of the covenant: faith, repentance and obedience. They then make public confession of their faith in Christ, or become covenant breakers, and subject to the discipline of the Church.

In these or the like instructions, the minister is to use his own liberty and godly wisdom, as the ignorance or errors in the doctrine of Baptism, and the edification of the people, shall require.

He is also to admonish all that are present to look back to their Baptism, to repent of their sins against their covenant with God; to stir up their faith; to improve and make right use of their Baptism, and of the covenant sealed between God and their soul.

He is to exhort the parent to consider the great mercy of God to him and his child; to bring up the child in the knowledge of the grounds of the Christian religion, and in the nurture and admonition of the Lord; and to let him know the danger of God's wrath to himself and child, if he be negligent; requiring his solemn promise for the performance of his duty.

The minister is also to exhort the parents to the careful performance of their duty, requiring:

a. That they teach the child to read the Word of God;

b. that they instruct him in the principles of our holy religion, as contained in the Scriptures of the Old and New Testaments, an excellent summary of which we have in the Confession of Faith, and in the Larger and Shorter Catechisms of the Westminster Assembly, which are to be recommended to them as adopted by the Church, for their direction and assistance, in the discharge of this important duty;

c. that they pray with and for him;

d. that they set an example of piety and godliness before him; and endeavor, by all the means of God's appointment, to bring up their child in the nurture and admonition of the Lord.

56-5. The minister shall then read the covenant promises:

For to you is the promise, and to your children, and to all that are afar off, even as many as the Lord our God shall call unto him. And I will establish my covenant between me and thee and thy seed after thee throughout their generations for an everlasting covenant, to be a God unto thee and to thy seed after thee. Believe on the Lord Jesus, and thou shalt be saved, thou and thy house. (Acts 2:39; Gen. 17:7; Acts 16:31)

The minister shall then propose the following questions:

1. Do you acknowledge your child's need of the cleansing blood of Jesus Christ, and the renewing grace of the Holy Spirit?

2. Do you claim God's covenant promises in (his) behalf, and do you look in faith to the Lord Jesus Christ for (his) salvation, as you do for your own?

3. Do you now unreservedly dedicate your child to God, and promise, in humble reliance upon divine grace, that you will endeavor to set before (him) a godly example, that you will pray with and for (him), that you will teach (him) the doctrines of our holy religion, and that you will strive, by all the means of God's appointment, to bring (him) up in the nurture and admonition of the Lord?

To the congregation (optional):

Do you as a congregation undertake the responsibility of assisting the parents in the Christian nurture of this child?

56-6 Then the minister is to pray for a blessing to attend this ordinance, after which, calling the child by name, he shall say:

I baptize you in the name of the Father, and of the Son, and of the Holy Spirit.

As he pronounces these words, he is to baptize the child with water, by pouring or sprinkling it on the head of the child, without adding any other ceremony; and the whole shall be concluded with prayer.