There are actually Dispensationalists in the Bible. They are the ones who thought the Lord was coming preaching what you all call the 'Kingdom Gospel'. They appear occasionally in the Gospel accounts (sometimes the Disciples themselves are Dispensationalists) and in early Acts, when they----even at the Ascension----still ask about the coming of the earthly kingdom.
The lesson of the New Testament is not to read the thing thinking the Dispensationalists are the protagonists, they're always either corrected or ignored; it's to notice that what everybody thought was coming, is not what was coming. The Lord brought the New Covenant to the earth, He was dedicating the 'New Testament' with His blood and body on the altar of the cross; our High Priest forever, in the order of Melchizedek.
Peter was one of the Dispensationalists in the Gospels, that's for sure. But part of the story of Acts shows how he came to learn the full nature of what the Lord was preaching when He walked this earth. It took at least one altercation with newly 'minted' Apostle Paul to set Peter straight, but afterward, there isn't any necessary indication that Peter was still talking about the 'Kingdom Gospel' in Acts or in his letters.
And remember Galatians was written very early in terms of New Testament books. What Paul recounted there was past, no later than the year AD 50. We don't have any reason to necessarily think that Peter didn't learn his lesson, and while it's granted that 1st Peter was written seemingly to particularly 'Jewish' church assemblies ('Jewish' here meaning any of Abraham's descendants, not just those of Judah, so including what are called 'Samaritans' in the Gospels as well), there is also a distinct lack of instruction to be circumcised, and there is a certain promulgation of the sacrificial death and Resurrection of the Lord.
Peace.
