No child should EVER be allowed near a dog when he is eating his meal. Being a first time dog owner perhaps you do not already know this but most dogs do not appreciate having their food stolen (whether or not your daughter was actually stealing food is not the issue, the dog sees it that way) and have a protection mechanism of sorts. The protection is guarding, if the ancestors of dogs had not guarded their food they would have starved to death. So some guardiness is built in to most dogs.
IMO your dog sounds reasonably tolerant otherwise your child would have received much more than a warning (as scary as growling and barking may be they are simply the dog "speaking" to us, telling us to stop our behavior, in a non-violent way). I'm sure the dog gave warnings the first time your child reached into the bowl, but they were more subtle (freezing, staring, bracing with his feet, putting head further into bowl to block the child, tightening lips, etc.). Then after those gentler requests to stop went unnoticed he felt the need to speak louder and clearer by growling and barking which of course worked wonders.
It is YOUR job to keep both your child and your dog safe from each other, this means making every effort to keep your child from upsetting the dog, she is far too young to understand dog body language or to follow proper dog etiquette all by herself, so you must do those things for her. Next time your child moves towards your dog while he is eating you should remove her and tell her to leave dogs alone while they eat. Then repeat.
However you should take steps to make sure the food guarding does not escalate, there does come a point where it goes from normal guarding to paranoid, excessive, dangerous guarding which could really get someone hurt.
During feeding time feel free to approach the bowl yourself and drop treats in (something better than his regular food like meat from your dinner). Or put down an empty bowl and approach the bowl to put in a handful of food, step back as he eats then repeat until he has consumed the normal amount.
Just remember to NEVER leave any dog alone with any young child, it is a disaster waiting to happen, they do not understand one another and neither are entirely predictable.
Good luck with your dog, to me his behavior sounds normal, just be sure to be more careful about the interaction between the dog and child. Stick around the forum and I'm sure we can help you in your journey with your very first dog!