This may sound terrible--but the best advice I ever got about teaching children came from some friends who raised horses. :)
We didn't have kids at the time, but these friends explained how they trained their prize horses and said they used the same techniques on their kids. Their kids were amazing. When they explained we were sold for life. (We've now raised three daughters with these concepts in mind and have never had a moment's "terrible twos" or "terrible teens" even from our fifteen-year-old.
The idea is: you don't reward behavior you don't want repeated. But if they give you even a step toward the right behavior, you IMMEDIATELY reward it with the response they're seeking.
So in your case--you would ignore the fussy behavior (except for saying "no!" rather firmly to let her know you don't approve), but the second she stops fussing (even if it's accidentally), you go and pick her up and hug her and let her down. That way you reinforce the idea that it's the quiet behavior you're looking for. The next time, you go a step further. You let her know it's the quiet behavior but maybe you also want her to take another bite of her supper first.
The key our horse-training friends taught us was that you can't expect them to go the entire way the first time, but you guide their understanding of where you want them to end up by rewarding the tiny steps along the way.