Check a few things before assuming it's tranny trouble. As already posted, motor mounts are pretty important in these vehicles and will certainly wear/degrade. You should certainly check the driveshaft couplers - one at the front and one at the rear. Another normal wear item that will cause the problem you describe. In other words, you need to get under there and inspect the driveline. If nothing is out of place or obvious, then a check of the tranny would be next.

Good luck.