You can actually skip the puree stage altogether and start out by giving them chunks of food to eat, there is a whole thread all about baby led weaning which has some great advice! Gagging is actually a good thing, she is learning to manipulate the food in her mouth in order to chew and swallow without choking - but it is scary to hear and hard to trust them
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We started doing finger foods at about 7 months along with purees. We started giving fingers of food like steamed carrot, green beans, baby sweetcorn, plums, ripe pear and anything which was soft enough to gum and "chip" shaped so he could hold it and control how much he took. In fact he did better with bigger chunks than tiny bits as he could bite/gnaw/suck at his own pace and manipulate the food more easily. With fruits like peaches and plums I would give slices and at first he would suck the flesh from the skin but soon he began munch the whole chunk.
What I would do now for your LO is what we do - he gets mushed/chopped food which I (and he now) spoonfeed and foods like veg which he eats himself. So you could carry on with purees but gradually start making the texture thicker and lumpier, give her food on her tray like carrot sticks, broccoli spears etc that she can pick up and experiment with. At first she may not actually eat anything but gradually she will take things to her mouth, suck, chew and eventually swallow.
Hope that makes sense!
Laura