Hi Vicki.
The choking thing is normal and scary to watch! It'll take her a few goes to figure out the size of food she can handle at once. Also they often gag pretty violently as opposed to choke, choking is silent and when you need to think about helping out
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Tbh both of my kids have dealt with actual choking fine, they make a few silent efforts before getting it out. The funniest was a week ago when this little piece of pear got coughed across the table, his eyes watered a little and he carried on! Big gagging noises are her figuring out how far down her throat she can shove it, which at this age isn't very far for a dramatic reaction. Does that make sense? Just try not to look worried when she does it or it might make her think she should be scared!
I agree with Megan, give her various sizes and see which she copes with better.
J finally mastered the pincer grip today and picked up a pea very gently
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He placed it gently in his mouth, sucked it, then smiled and it fell out!! He managed to chomp one into pieces before expelling that too, then he had a quick game of tiddlywinks with a few!!!