The Currently Most Accepted Model
(Via the Saudi Arabian Peninsula)
After Lehi's son, Nephi "worked the timbers" (i.e. it wasn't a raft) (I Nephi 18:1-2) and built a boat, they stocked it and put to sea. The local trees are possibly adequate for planking, but would never work for the keel, mast, or spars. Untreated wood is eaten by water worms there.
For the first 4,000 miles they would be traveling mostly against highly variable winds and currents.
At an average of 2-3 miles per hour, the first 4,000 miles would take 1,333 - 2,000 hours or 8-12 weeks.
The second 4,000 miles would have brought the ship ever closer to land. For hundreds of miles the signs of close-by land would have been unmistakable -- tree branches on the water, land birds in the air, etc. Close to the end of this second 4,000 mile they would have passed within 13 miles of land. By this time, if they were making very good time (and there are several historical reasons to doubt this), they would have been at sea at least 4-6 months. With this group's tendency toward rebellion, with land so close by, the account would not have missed the resultant mutiny (I Nephi 18:9-22).
The last 9,000 miles would have been the most difficult. They now would be sailing directly against the prevailing winds and currents. At one mile per hour (in the right direction), they would have been speeding. Some have said that they could have ridden "El Niņo", but even that would have been of little help. El Niņo does reverse the prevailing winds and current near the equator, but only weakly (less than 1 mile per hour), narrowly (about 100 miles wide), and only for a few months.
9,000 hours = 54 weeks or just over a year.
In short, They would have been very lucky if they completed the voyage in a year and a half to 2 years leaving from the Saudi Peninsula.
Final leg 9,000 miles