Hi J..
First, any sort of solids before 12 months is just practice. Baby's primary calories need to come from formula or breastmilk until they are 1 year old.
Next, it could be there is some sort of discomfort with eating. Whether she bit her lip, or bit the spoon, or maybe the cereal is just causing some sort of internal discomfort. Is she pooping normally?
Also, you CAN introduce table foods when they are about 6 months old. Of course you have to be careful with what you offer. You can go giving her a raw carrot and expect her not to choke. SOFT cooked veggies, rice cake, bread crusts... stuff like that are ok. Google 'baby led weaning' and you will get some info.
Purees are just as much as choking hazard as anything else. Many babies try to 'drink' the puree off the spoon and then it gets forced to the back of their throat but of course is much thicker then the milk they are used to.
Babies develop the 'chewing' skill about the same time they develop the reach out and 'rake' thing back to them skill. (which typically happens around 6 months). Just and FYI, the other reason to wait until at least 6 months for solids is because there is increasing evidence to suggest their digestive tracks just can't handle the solids and introducing them sooner can lead to problems late in life like IBS.
Anyway, solids aren't necessary at this point. I would back off until she gives you more signals she is ready... like trying to take your food etc... And I would think about offering something other then purees.
By offering table food you are introducing the REAL tastes and textures of the food. My daughter is 10 months old (almost) and has had: parnsip, broccolli, zuchinni, pear, apple, wheat bread, shredded cheese, banana, carrot, white asparagus, plain yoghurt, and egg yolk (even french toast sticks made with egg yolk). As long as you sit there with them while they eat, and things are soft cooked things are fine. Their gums are very strong and can 'chew' soft cooked things.
Good luck.