Yes, specifically the Eternal Kingdom begins with the establishment of Christ’s eternal reign initated by the advent of the Millenium. At that point His reign over the earth is eternal even though challenged very shortly at the end of His Millenial Reign. As noted in Daniel below, at the conclusion of the 70th week when Christ crushes the final beast empire his “kingdom which will never be destroyed” begins. So yes, the Millenial Reign is not eternal as it’s specifcally defined as 1,000 years in length, however it is contained within His eternal reign as from that point forward His Reign or Kingdom will never end.
In the days of those kings the God of heaven will set up a kingdom which will never be destroyed, and that kingdom will not be left for another people; it will crush and put an end to all these kingdoms, but it will itself endure forever. 45“Inasmuch as you saw that a stone was cut out of the mountain without hands and that it crushed the iron, the bronze, the clay, the silver and the gold, the great God has made known to the king what will take place in the future; so the dream is true and its interpretation is trustworthy.”
But the day of the Lord will come as a thief in the night, in which the heavens will pass away with a great noise, and the elements will melt with fervent heat; both the earth and the works that are in it will be burned up. (2 Peter 3:10)What is the day of the Lord, and how do you squeeze a millennial kingdom into Peter’s timeline?
Then we have to examine what Paul says about Christ’s kingdom.
21 For since by man came death, by Man also came the resurrection of the dead.Paul tells us the “the end” coincides with Christ’s coming and the resurrection of the saints. At His coming He delivers up the kingdom to the Father, vanquishing death. In 1 Thessalonians 5, Paul tells his readers that Christ comes “as a thief in the night,” and warns them to be prepared, “Therefore let us not sleep, as others do, but let us watch and be sober.” This would fit with Peter’s picture of the “day of the Lord” coming as a “thief in the night” initiating the new heavens and new earth.
22 For as in Adam all die, even so in Christ all shall be made alive.
23 But each one in his own order: Christ the firstfruits, afterward those who are Christ's at His coming.
24 Then comes the end, when He delivers the kingdom to God the Father, when He puts an end to all rule and all authority and power.
25 For He must reign till He has put all enemies under His feet.
26 The last enemy that will be destroyed is death. (1 Cor. 15)
Postmillennialism is an interpretation of Revelation chapter 20 which sees Christ's second coming as occurring after the “millennium,” a golden age or era of Christian prosperity and dominance. The term includes several similar views of the end times, and it stands in contrast to premillennialism (the view that Christ’s second coming will occur prior to His millennial kingdom and that the millennial kingdom is a literal 1000-year reign) and, to a lesser extent, amillennialism (no literal millennium).
Postmillennialism is the belief that Christ returns after a period of time, but not necessarily a literal 1000 years. Those who hold this view do not interpret unfulfilled prophecy using a normal, literal method. They believe that Revelation 20:4-6 should not be taken literally. They believe that “1000 years” simply means “a long period of time.” Furthermore, the prefix “post-” in “postmillennialism” denotes the view that Christ will return after Christians (not Christ Himself) have established the kingdom on this earth.
Those who hold to postmillennialism believe that this world will become better and better—all evidence to the contrary notwithstanding—with the entire world eventually becoming “Christianized.” After this happens, Christ will return. However, this is not the view of the world in the end times that Scripture presents. From the book of Revelation, it is easy to see that the world will be a terrible place during that future time. Also, in 2 Timothy 3:1-7, Paul describes the last days as “terrible times.”
Those who hold to postmillennialism use a non-literal method of interpreting unfulfilled prophecy, assigning their own meanings to words. The problem with this is that when someone starts assigning meanings to words other than their normal meaning, a person can decide that a word, phrase, or sentence means anything he wants it to mean. All objectivity concerning the meaning of words is lost. When words lose their meaning, communication ceases. However, this is not how God has intended for language and communication to be. God communicates to us through His written word, with objective meanings to words, so that ideas and thoughts can be communicated.
A normal, literal interpretation of Scripture rejects postmillennialism and holds to a normal interpretation of all Scripture, including unfulfilled prophecy. We have hundreds of examples in Scripture of prophecies being fulfilled. Take, for example, the prophecies concerning Christ in the Old Testament. Those prophecies were fulfilled literally. Consider the virgin birth of Christ (Isaiah 7:14; Matthew 1:23). Consider His death for our sins (Isaiah 53:4-9; 1 Peter 2:24). These prophecies were fulfilled literally, and that is reason enough to assume that God will continue in the future to literally fulfill His Word. Postmillennialism fails in that it interprets Bible prophecy subjectively and holds that the millennial kingdom will be established by the church, not by Christ Himself.
When you get this, along with the belief that all prophetic Scripture was fulfilled in 70AD, you going to get rage on threads which prove that God's word, taken as He wrote it, not tampered with and not allegorized, is true and inerrant and is in the process of coming to pass.
This is par for the course.