As early as needed. It is hard to diagnose pollen allergies in a baby, particularly one that is exposed to viruses in daycare and may do a lot of sneezing due to infections. Skin testing can be done at any age, but the immune system doesn't start making allergic antibodies until about six months of age. If there are allergic symptoms and positive skin tests before that, it is due to antibodies transferred from mom.
Depends. Anyone can be tested anytime for any allergens. The question is what is medically appropriate and justified. In general, babies will become allergic to indoor allergens first (dust mites, furred pets) and possibly foods (in the appropriate disease state) and over the course of time (years) if they have rhinitis and asthma they can develop season pollen allergy.