My 3 year old daughter has a temperature of 104.7, I gave her children's tylenol (acetaminophen) but she vomited it up immediately. Should I take her to the doctor?

Emergency. Yes. This is an emergency. This temperature is too high to wait. Please get her to an urgent care center or emergency room quickly. If in doubt, then please call or page your pediatrician for instructions.
May be! How your child is acting will give you a good idea of whether a minor illness is the cause or if you should see a doctor. If your child is still playing , eating and drinking well is alert and smiling at you has a normal skin color looks well when her temperature comes down the illness is probably not serious try cooling her body with tepid water. If she looks really sick see the doctor.