Popping in to agree with pps regarding choking and to add that a LOs gag reflex is much further forward than an adults so the chances are that she will gag first (and more frequently), this is totally safe and normal and means she is doing exactly the right thing, bringing the food back to the front of her mouth where she can chew and gum on it. Gagging is a bit scary but it is not blocking LOs air way. Stay calm so that LO doesn't get upset.
It's also not advised to try to pull food out of LO's mouth with your fingers (in case you feel tempted) as this can inadvertently push it into a choke position.
I went on an infant first aid course to find out what to do in case of a choke, you could probably just as easily watch a free video on line to get the info.