I let DS graze and eat on the run, he also doesn't like to sit still! I used to hate my eldest 2 walking around with food but DS3 just doesn't stop so I gave in and let him eat while he's on the move.
I wouldn't like to go high protein either, maybe just a little more dairy if she likes it she can munch on a piece of cheese while she's on the go, maybe extra milk in a sippy cup. Dairy would help with her weight if you want her to put on a bit but if you're not worried I'd keep doing what you're doing