“In terms of infant baptism, Peter baptized the whole household of the centurion, which would have included infants, and circumcision is a type of baptism.”
You left out the hh of the Philippian jailer (Acts 16:33), but in either case you cannot say this included infants unless the text gave sufficient evidence, rather than the only information we have indicating the opposite.
In Acts 10:24 we see the household of Cornelius being described as “his kinsmen,” and later that “the Holy Ghost fell on all them which heard the word”, and that they spoke with tongues, and magnified God (vs. 44, 46). Thus if anything is indicated as regards the age of coverts, it is that they were mature enough to heard and speak.
In Acts 16:32 we read that Paul “spake unto him the word of the Lord, and to all that were in his house, and in v. 34, that the jailer “rejoiced, believing in God with all his house.” Again if anything agewise is revealed it is that they were all able to hear and respond.
There are other references to households being baptized, that of (Lydia) Acts 16:14, 15), but it is very doubtful that Lydia had nursing children, seeing as she traveled on business some 300 miles from her native city, and mention of even a living husband is missing. This no substance is provided that would allow an assumption her household included infants. Nor in the case of Stephanas (1 Cor. 1:16). And as the Holy Spirit lays down requirements for baptism that exclude infants, and only provides evidence that souls were cognitive of their need for Christ and able to respond (Acts 2:37; 8:12, 36-38; 9:1-6; 16:14, etc.), the need for at least one specific example of paedobaptism is critical, and the lack of which is exceedingly conspicuous, considering the gravity of the act.
Faced with such absence, Col. 2:11, 12 is invoked in an attempt to transfer the time of the O.T. practice of circumcision into the New Covenant. But while the baptism is inferred to correspond to circumcision, there are critical covenantal distinctions between the two, which prevent paedobaptism.
Circumcision was an external sign of the Abrahamic covenant that was commanded to be performed to all the household, servants included, but only for the males, and without a personal faith being a prerequisite (Gn. 17:10-14). It was given only for males because being a partaker of the covenant was hereditary.
One the other hand, baptism is an external expression of inward effectual faith, for both males and females, in which one’s own personal faith is a prerequisite. While almighty God clearly commanded circumcision to be performed to all the household, without a faith requirement, He commands the church to preach “repentance toward God, and faith toward our Lord Jesus Christ” (Acts 20:21; cf. Lk. 24:47), with this being a prerequisite for baptism (Acts 2:38; 8:36-38).
Rm. 4:11 is supposed to help paedobaptists, but it shows Abraham believed before he was circumcision, which would show baptism is not necessary for salvation, but it does not lend itself to justifying baptizing ignorant souls based upon their parental faith, for the above reasons.
Another attempt is to use 1 Cor 7>14, but the sanctification there is based upon the faith of one spouse, and the sanctification also includes the other unbelieving one.
Finally, evidence indicates paedobaptism was a later development in church history, but to be Biblical it to hold to the prerequisites for baptism, repentance and whole hearted faith.
I could say more, but it is late here. Forgive any typos.
I forgot to mention the duplicity of paedobaotists who use Col. 2:11, 12, as they refuse to allow infants to take part (by eating) in the the Lord’s supper, whereas in the Passover it was for the whole family, male and female (Ex. 12:1-20). Christ is explicitly declared to be our Passover ((1 Cor. 5:7 - though perhaps the “Last Supper” was not a Passover meal) and the Passover manifests more correspondence to the Lord’s supper than circumcision does to baptism, The reason why paedobaotists do not give it to infants is because the prime requirement for participation in this is that of self examination (1 Cor. 11:28), which an infant cannot do. Yet neither can an infant fulfill the stated requirements for baptism.
In addition, i might further contend, for those who hold that baptism removes original sin, that (in addition to personal penitent faith being that which appropriates justification) this is not necesary for infants, as God does not judicially punish the innocent for the sins of the guilty, infants for the sins of their fathers ((Dt. 24:16; 2 Chr. 25:4; Jer. 31:30; Ezek. 18:20). Though we all realize the temporal consequences of others actions to varying degrees (Ex. 34:7; Jn. 4:38), yet the great white throne judgment is distinctly declared to be “according to their works” (Rv. 20:12, 13) - not according to their fathers.
Of course this is problematic for Calvinism as well, but the only way i can see to reconcile a need for infants to be forgiven is if it can be demonstrated that in some way they were culpable of Adam’s sin.