Hi Shelley!
Rides at Disney are primarily based on height, not age. For example, a number of rides have height requirements of 40" or 48" and such.
This would be a parent judgment call, so you would need to use your discretion on whether they're old enough (or responsible enough) to get on a ride by themselves.
Disney is a fun place, but safety should always be a priority. Of course, I'm probably a little over protective, but then again, my kids are 3 and 7. But who am I kidding? I'll be over protective when they're 37! :-)
Again, just use your discretion and what you feel is best concerning your kids.
And have a terrific time!