Here's a breakdown of the timeline:
* The Fellowship set out from Rivendell on December 25th of the year 3018 of the Third Age.
* The Fellowship was broken in the Mines of Moria in February 3019.
* Frodo and Sam arrived at Mount Doom on March 25th, 3019.
* The Ring was destroyed on March 25th, 3019.
This means the journey from Rivendell to Mount Doom took approximately 15 months (December 25th, 3018 to March 25th, 3019).
Adding the time spent by the Fellowship before breaking up in Moria, the total journey time would be approximately 17 months.
However, it's important to note that:
* The actual time spent in Moria is not explicitly stated in Tolkien's writings.
* The Fellowship didn't travel in a straight line, and their journey was fraught with challenges and delays.
Therefore, the exact duration of the journey can only be estimated based on the available information.