Also it's a good idea to make sure kitty is doing well since she's in contact with your other pets. Plus you want to make sure she gets her vaccinations, which she should probably be getting before February.It is not normal for kittens to vomit. Causes for vomiting could be parasites (roundworms are notorious for this), food allergy/intolerance or other medical issues.
Do you know when your kitten was last dewormed?