Toy Story can get a little whippy, but I've taken my dd on it with no problems since she was around 2months old. At first, I kept her in the Ergo and held her head at the turns. That's something you can certainly do with a 7 month old if they like the carrier. With her, I think she was on my lap by that age and I just held on extra tight. She's 2 now and hasn't been on it in a few trips, but the last time she rode it, I'm pretty sure she was just next to me with my arm around her.
As far as other rides, all without height restriction are fine for a 7 month old. Like pp mentioned, I wouldn't go crazy on the teacups, but that's probably common sense. Most rides let you wear the baby, if you want and let them be on your lap. Rodger Rabbit is one that the will not do either. I learned that the hard way! At 7 months old, dd hadn't developed a fear of any rides and it was so much fun to watch her look around and really start paying attention to her surroundings. That's when she fell in love with Small World! She has since stopped liking faster movement, which makes it hard.