Make sure your trans fluid isn't milky or burnt smelling. Auto transmissions are killed 99% of the time by excessive heat or dirty fluid. Dirty fluid could mean broken down oil, clutch shavings, coolant contamination, etc. When you get a chance, or after you replace the trans, the best things you can do for an auto trans are install a sufficient external cooler(with new lines) separate from the radiator, fill with 100% synthetic fluid such as Royal Purple MaxATF or Amsoil (they won't break down), and put a shift kit in the valve body for best clutch engagement.
My trans fluid was milky with coolant and absolutely filled with scary dirt and residue. I now have a large trans cooler meant for heavy towing, 2nd stage shift kit, and new fluid/filter. Won't get synthetic until I rebuild it, due to cost, but it makes excellent firm shifts now without any problems. Also put a drain plug at the pan for a less messy job.
The transfer case is very simple to fill if you have a fluid transfer pump. Walmart has nice ones for $7, and it only takes a small amount of auto trans Dex fluid. Drain at the drain plug, fill at the fill plug. You could even use synthetic here for added protection, not as bad as the 10+ qts in the trans.
Finally, it is very important to make sure the engine cooling system is in good shape. To do this, you can flush the radiator, add new 50/50 coolant, and put in something like Royal Purple Purple Ice additive. This won't hurt the system at all, but it helps keep things cool. You also need to be sure that the temp gauge is performing correctly, as it is the only thing warning of failure. Check thoroughly for leaks all around.
These things may not be totally necessary before the trip, but it's at least good to eliminate leaks and have good, clean fluid. Definitely look into all new fluids soon though. If you've already made the trip, I hope it went well!