At what age can you have your child allergy tested for respiratory allergies?

Any age. There is no age below which children cannot be tested for allergies. Skin reactivity improves with age, so negative tests may not completely exclude an allergy, but that is not a reason to delay testing.
Any age. There is no lower limit or upper limit to when one can be tested for allergies. The question is what will be tested for and that will vary by patient, symptoms and age.
Early childhood. Allergies to pollen, mold, pet danders, etc. Can be tested for as early as 2-3 years of age (sometimes even earlier, if indicated).