I cut and pasted this article from the Mayo Clinic website.
Question
Air travel with infant: Is it safe?Is air travel safe for an infant?
Answer
from Jay L. Hoecker, M.D.
Air travel with an infant typically is safe. However, there are medical and safety issues to consider. A doctor may advise against unnecessary air travel during the first two weeks of life, when a newborn's body is still adjusting to life outside the uterus — and is especially vulnerable to the germs that circulate in the aircraft's recycled air.

Parents may worry that air travel will hurt their child's ears. But the effects of flying on an infant's ears are the same as for an adult's ears. Changing cabin pressure causes temporary changes in middle ear pressure, which can result in pain. Sucking helps equalize the pressure in the ears. For this reason, feeding the infant during takeoff and landing may help. If your baby isn't hungry, try offering a pacifier.

An infant with a recent ear infection may be very uncomfortable when flying. Check with your child's doctor before leaving if you have concerns. Your doctor may provide you with pain-relieving eardrops, in case your baby experiences ear pain.

Some parents worry that air travel increases the risk of sudden infant death syndrome (SIDS). This concern may stem from an old (1998) British Medical Journal report in which researchers tested the effect of lowered oxygen — such as in a pressurized airplane cabin — on infants and found that irregular breathing was more common. However, there's no evidence that air travel causes SIDS.

If you travel on an airplane with an infant, the American Academy of Pediatrics recommends that you place the child in a rear-facing child safety seat that's properly installed and secured in the seat next to yours. Most child safety seats are certified for air travel. Check the label if you're not sure. According to the Federal Aviation Administration, child safety seats shouldn't exceed 16 inches wide for the best fit in aircraft seats — especially in smaller commuter aircraft. If you can, choose a bulkhead seat and avoid being seated in emergency exit rows.

To make air travel easier with your infant, pack a teething ring, pacifier, special blanket or stuffed animal, and age-appropriate toys (such as rattles or plastic rings) and books in your carry-on bag. If your baby is fussy during the flight, taking a brief walk up and down the aisle may help.