That's not really big, as aloes go. It'll get twice that big even in that little pot. However, I'd recommend transplanting it into a wide shallow pot, just so it isn't so easy to knock over. They're more-or-less a cactus, and thrive in well-drained, nutrient-poor soil. Anything just north of beach sand will do. I've grown them in everything from garden soil to paver base and they've always done just fine. I would assume cactus mix is probably best, but I'm too cheap to find out. Don't worry too much about transplant shock, they can bounce back from just about anything short of being completely pulverized.