Gagging can be alarming to watch but it's a necessary part of learning to move food around the mouth with the tongue. If you learn how to deal with real choking then you might feel more confident about your daughter's ability to deal with larger-than-wise chunks.
My 12 month old was traditionally weaned and enjoys feeding herself but with things like bread she can't seem to regulate how much she puts in her mouth and ends up getting into difficulty which frightens me so much. Is it ok for me to cut food into manageable pieces or would this be holding her back? I see other children her age eating sandwiches so I feel like I'm doing something wrong.