Peter's reference is to Psalms 90:4:
4 For a thousand years in Your sight Are like yesterday when it passes by, Or as a watch in the night.
This is a comparison of time IN GOD'S sight, which tells us Peter's message here is not a literal 1000 years.
Take a look at Deuteronomy 7:9:
9 Know therefore that the Lord your God, He is God, the faithful God, who keeps His covenant and His lovingkindness to a thousandth generation with those who love Him and keep His commandments;
There "a thousandth generation" represents eternity.
Again in Psalm 50:10:
10 “For every beast of the forest is Mine, The cattle on a thousand hills.
In this verse "a thousand hills" means all hills
This is how God uses 1000 to represent eternity, or an undetermined number.
This is how John is using Christ reign of a thousand years to represent and undetermined amount of time in which Christ will reign, and that period started after His resurrection.
John uses it differently when it comes to the 144,000 of Revelation 7:4-8, where he sees 12,000 from the tribes of Israel.
To see who they are one has to see the pattern visions to John in this prophecy. Throughout Revelation John will hear something, and the he will look at something to describe what that which he saw means.
Revelation 7:9 tells tells us who the 144,00 is:
9 After these things I looked, and behold, a great multitude which no one could count, from every nation and all tribes and peoples and tongues, standing before the throne and before the Lamb, clothed in white robes, and palm branches were in their hands;
So the 144,000 are the Israel of God, they are not fleshly Israel, but spiritual Israel. They have circumcised hearts and are the TRUE ISRAEL OF GOD as well as THE TEMPLE OF GOD built on the apostles and prophets, with our Lord Jesus as the cornerstone!!!