The end time (also called end times, end of time, end of days, last days, final days, or eschaton) is a future time-period described variously in the eschatologies of several world religions (both Abrahamic and non-Abrahamic), which believe that world events will reach a final climax.
The Abrahamic faiths maintain a linear cosmology, with end-time scenarios containing themes of transformation and redemption. In Judaism, the term "end of days" makes reference to the Messianic Age and includes an in-gathering of the exiled Jewish diaspora, the coming of the Messiah, the resurrection of the righteous, and the world to come. Some sects of Christianity depict the end time as a period of tribulation that precedes the second coming of Christ, who will face the Antichrist along with his power structure and usher in the Kingdom of God.
The Merriam-Webster definition of doomsday is as follows:
1 : a day of final judgment
2 : a time of catastrophic destruction and death
Therefore, your interpretation of the end of days as meaning doomsday is accurate.
As mentioned in a comment under your question, the Free Dictionary entry you link to refers to a syntactically similar phrase but one that means something quite different.
In the following quotation, I have put the possessives used in bold text.
to the end of (one's) days (redirected from to the end of our days)
Forever; until the day that one dies. For his heinous crimes, the murderer is going to be locked away to the end of his days. Baby, you know that I'll love you to the end of my days!