There is not a short answer to your question. Allergy testing is not as simple as getting a blood test, and you want to make sure the symptoms that the child has are significant enough to warrant going through the whole process. It involves pricking the skin multiple times, and applying substances that may cause swelling and itching. This could be a very difficult, anxiety provoking situation for a two- or three- (or even four-) year-old.

You also have to ask what the testing results will really tell you. I'm assuming that you are not talking about food or drug allergies but rather allergies to things in the environment. The vast majority of children who have chronic allergy symptoms are sensitive to dust mites, molds, and animal danders in the house. (This is different from seasonal allergies which occur from pollen exposure). The way to prevent symptoms is to limit the exposure to these agents: Plastic covers for the mattress, use synthetic pillows, get the stuffed animals off the bed and washed regularly, no carpet on the floor, keep dust to a minimum. You may find that her symptoms improve quickly with these measures.

If your child has severe allergy symptoms such as recurrent episodes of wheezing, sinus infections, snoring and sleep apnea, it may indeed be worthwhile to do the testing, even at this age. I suggest that you assess the severity of your child's allergy symptoms and the circumstances in which they occur, and then talk with the allergist or your pediatrician about the options.