Cautionary tale..my daughter started gymnastics at age 3. We moved into an area with horrible winter weather in November. Didn't know anyone, my eldest was in elementary school and my 2 and 3 year old were driving me crazy inside the house. I needed an outlet for them, so I started them in toddler classes. Long story short, one of the coaches noticed my daughter quickly could do a pullover by the age of 4 (we started 2 months before her 4th birthday). She also could easily walk the high beam, she could do a chin up hang, and she could jump in straight jump, tuck jump, straddle jump on trampoline, and was really good at being coordinated. The coach said, "She is a kid the old Russian coaches would send to camp!" (sorry if that offends anyone, but that is what was said). We stayed in gymnastics and she loved it. One of the coaches then suggested we put her in Jr. TOPS. Now, I was never a competitive gymnast. I did rec gymnastics as a kid and loved it, but it was too expensive and time consuming for my family to consider. So I said, sure, Jr. TOPS sounds great, she loves gymnastics.
Fast forward 8 months and my 5 year old is getting stomach aches before practice. She is rushing from kindergarten to 2 hours of practice twice a week and not getting home until 8pm. It was a disaster. Sure she got stronger. Sure she got great shaping, but she didn't learn any skills. TOPS was developmental and a lot of conditioning, so what someone said earlier about skills not coming until level 3, for us that was the case. It made my daughter hate gymnastics because it was work not fun.
As you can see, she went back, but it was at a different gym after almost a year off and she missed it. I didn't tell them she had been in Jr. TOPS and I started her in rec classes. She just wanted to do gymnastics. Eventually they invited her to team and she started level 3 at age 7 after I had many conversations with the compulsory coach that no matter what I wanted gymnastics to be fun for her. She is now a level 7, training level 8, and we left a gym because it became about winning and work not about gymnastics and personal growth (that's another story).
Moral of the story, she has plenty of time. Don't push her to be a gymnast yet. Let her be a toddler.