I do this as does my husband. My kids do too. It's normal. Some people are just sensitive to gross things and textures that they find disgusting.
However, if you're finding that she's suddenly sensitive to a lot of different tactile textures and things are making her gag to the point that it's interfering with daily life... then you may need to have her evaluated for a Sensory Processing Disorder aka Sensory Integration Disorder. Gagging because she has a piece of banana on her finger shouldn't elicit a gag reflex.
A friend has a daughter (does not have Autism) that gagged and threw up when they put shaving cream on her hand. They were playing with different textures and were shocked when that happened. She couldn't eat ice cream with whipped cream... the texture made her throw up. She has a lot of issues with food and clothes because she's so very sensitive to textures. And I can relate because I have a daughter (on the Autism Spectrum) who also has Sensory Processing Disorder (related to the Autism)and self-restricts her diet because of tactile textures.