Matthew tells us that the Transfiguration happened "after six days"- i.e. on the seventh day after Jesus' promise that "some will not taste death until they see the Son of Man coming in his kingdom in power." At this time, the seventh era of the world was viewed by many Jews as being the age of Messiah and the Sabbath of the world-in other words, the coming of the kingdom of God. Jesus' hearer will now see what the kingdom is and about.
The seventh day is also the day of rest and Jesus brings that rest: "Come to me all of you who are heavy laden and I will give you rest." Rest is what happens when you receive the promise- hence the day of Sabbath- that is the day of the reception of the Word. This is also why the 49th year was a year of Jubilee and Daniel predicted "seventy-sevens" when the Messiah would come. This is the same day that the prophet speaks of in Isaiah 61: "The Spirit of the Lord is upon me . . . to proclaim the year of the Lord's favor"- i.e. a final Jubilee.
On the Mountain of Transfiguration, they see Jesus with the two great prophets of the OT. Then he appears in glory. Not only does this show that Jesus was the one they encountered in their OT theophanies, but it also suggests that Moses and Elijah are like the angels on the Ark of the Covenant that the kavod appeared between (Jesus is the kavod, since he reveals that he is the hypostatized Glory of YHWH). Jesus also appears between two person on the cross. Two angels also sit in his tomb, one on the top and the other on the bottom where he lay. So, he is the concealed God who appear in the cloud of incense and he is the sin-offering of the Day of Atonement. He is the "mercy seat" as Paul puts it in Romans 3. He is the place that gives rest, because he is the place where God is both most present, most concealed, and propitiated with blood. Again, he is the one who makes passive and gives rest through his forgiving word of promise in his blood.
Therefore Peter has the wrong reaction. He wants to build "Tabernacles" for Jesus and the other two. It is the Sabbath, why work? Jesus is the one who gives rest- why work? Jesus is the son of David who builds the "house for my Name," (a Temple/Tabernacle!) not you! He was the builder of the original creation, which Genesis describes as a cosmic Temple. He is the builder of the eschatological Temple, the Church. As the creator God and Temple-building son of David. Therefore it makes a lot of sense that he would be a carpenter!
In a word, it is Jesus who builds and not us. So, Peter is wrong to want to build, rather than receiving his building. After all, Jesus has just told Peter that he will build the Christian Church on the faith that he represents "on this rock I will build my Church..." Jesus is the one who builds Peter up into the eschatological Temple "built on the apostles and prophets, with Christ the chief cornerstone" and not Peter!
God does not want work, but to listen and be passive. The Father appears and silences Peter: "This is my beloved Son, listen to him." Peter will do a similar thing later. He will promise his own death to Jesus. But again, Jesus isn't the one who you actively die for, but one whom you passively die with when he dies for you. Peter tries to be active and fails. It is only in recognizing his sin and listening to the word of promise, that he is placed in the right relationship with Jesus.