Call each of the gym clubs and find out when they have classes scheduled for beginners at age 4. Go watch a few of the classes at each gym to see which, if any, seem to be a good fit for your daughter.
The next step, if an over-all program seems a fit, is to see if they'll allow your daughter to come in for trial classes. Try to set one up with each of the instructors that teach in the 4yo program, and see if she clicks especially well with a particular instructor.
I know it seems a lot do, but it may save heartburn and heartache in the future.
Have fun!