I hope your DD didn't hear the coach say that??
The way that you describe the coach said this sounds very inappropriate. I can understand if a coach does see noticeable / ongoing weight (fat) gain in a gymnast, that there might be real concern about being able to keep up the required strength to safely execute moves. And if a gymnast was indeed falling behind, a sensitive discussion privately with the parent only could be OK to gauge if there were any medical reasons or other concerns regarding the weight gain. But to 'accuse' a parent of bad nutrition based on a (as described) small kid belly that is very normal for 6-7 year olds, and to predict limited performance to boot, is out of line, in my opinion.
On the other hand, if you yourself are not sure about the proper nutrition for your child athlete (since you mentioned 'you don't know if her current diet is a good or bad thing'), then by all means seek nutritional advice. Not all children have the same exact needs, and athletes have special needs. I'm guessing you're not letting her eat donuts, french fries and cheetos every day. But whatever her diet, if you're concerned it's not optimal for her, then seek advice. For example, I have increased the protein and good fats for my 2 gymmies as their hours have gone up, and added an extra snack time.
You should definitely do as others have said and bring this up with the HC or owner. That coach should not be disparaging little girls for their physique.
Best,
s