I have to address one post -- It is not true that you must start at 3 to dance properly. We attend a lot of ballet performances and one company frequently interviews dancers after the show, on stage. Many of these professionals started lessons at six or eight or in some cases 10 or older.
But you're not asking about whether your chiild is going to be a prima ballerina! She just wants to dance. Yes, many "ballet" classes for kids this age are actually "creative movement" -- and that is just fine. Let her try it.
Look for a program that teaches children appreciation for the music; the concept of moving in time to music; flexibility; and creativity. Try local dance schools but also try your local recreation centers for this age; rec centers or community centers often offer shorter classes (six or 10 weeks, etc.) that let your daughter test out how she likes things. Keep signing up for the next session if she likes it. These classes are usually inexpensive -- It sounds like you might be concerned that dance will be expensive at this level but it's not.
When she's about five, six or seven, if she really is turned on by dance, look at local dance schools. Be aware that there are very different types of schools. Some are all about just ballet. Others are into "dance teams" that do jazz/hip-hop/"Broadway dance" and go to competitions. Yet others offer a variety of styles but don't do competitions. (I'm not a fan of the competitive dance team thing but some kids love it; my daughter is interested really only in classical ballet but also takes a modern dance class and likes that. However, she's 10 so is better able to make her own choices about dance.)
At your daughter's age she should just have fun, move around a lot, learn some very basic steps and enjoy the whole process. I would not worry about "I'll spend the money later." She will benefit from kinderballet or creative movement or kiddie ballet and tap programs now, even if she decides later to move on to another interest. The benefits are body awareness, coordination, appreciation for music, and a positive experience using their bodies and their creativity.