Possible, yes. Recommended, no.
OD may be nice but the auto in 03+ TJs (97-06 wrangler) is the 42RLE which is a piece of crap. It is a FWD car transmission (for "LH" cars, Concorde/Intrepid) that was converted to RWD/4WD and used in Jeeps. This was a weak and failure-prone transmission in the cars it was designed for and performed even worse in Jeeps which were much heavier than it was designed for and subjected to abuses well beyond what it was designed for.
The "old" 32RH (3-speed torque-flight) in your 01 is a much better transmission from a reliability/durability standpoint.
Better options if you want to replace the trans would either be a manual (AX15/NV3550/NSG370), an AW4 out of an XJ Cherokee, or a GM 700R4 (aka: 4L60/4L60E). There are a ton of write ups on all of these, a quick search (I.E. AW4 in TJ, 700R4 in TJ, etc.) in your favorite search engine should give you all the info you need.