Dogs are allowed, or at least this website confirms it:
http://www.austinexplorer.com/Hiking....asp?HikeID=23
I've been to Enchanted Rock a couple times and it's one of my favorite places in Texas. You and your friend shouldn't have a hard time getting to the top. The difficulty is pretty much up to you, as there are some very gentle slopes to the top or you can boulder your way up if you want.
Have fun, it's a great spot.