Hi, I recommend a trampoline. Maybe an indoor one with a bar. There are small little tykes bounce houses for less than 200 that are small enough to fit in a house. I let my girls rollerblade and ride their scooters through our house at that age. Oh and a skateboard was in the house. They were always riding on it. Horseback riding uses all the muscles in the body, so that one is good, too. Lots of musical chairs or dancing works, too.
How can I get DD more physical activity? Hobby? - Page 2
My son has ASD and loved hippotherapy. He did it once a week for three years and it was, bar none, the best therapy he ever received. Hippotherapy is not just riding a horse, his therapist did speech, OT, and sensory integration while he was on the horse and it's also great for building core muscles. Yes, it's pricey (about $30 a session), but we were able to receive a grant that covered it. Some insurances also cover it as an OT service.
List of IL hippotherapists: http://www.rush.edu/rumc/page-1239655964349.html