I agree with everything so far! We flew with DD1 at 2 months, 4 months, 6 months, and 1 year. I think that 2.5 months is actually one of the easiest times to fly with a baby, because they still sleep a lot!
Baggage Check-In/Ticketing:
I also always bring a copy of the baby's birth certificate AND immunization records. Southwest Airlines requires one of these documents as proof of age, but I take both just in case!
Every airline has different requirements as far as which baby items are considered "freebies" and which ones aren't. Car seats and strollers usually fly for free, but if you're taking a pack-n-play, that's hit-or-miss. Check the website before you go!!!!!
TSA Security:
You ARE allowed to bring breastmilk on the plane in bottles. If you do, make sure the bottles are clear, because that increases the chance that they will be able to use the electrical scanner instead of having to open the bottle up. The other two ways that they check for explosives are to open the bottle and hold a little sensor above it or to dip a strip into a sample of the milk (which they will pour out... and I think this is an older method, so you prob won't have to deal with this). Also, I usually put an ice pack in with the breastmilk, but I make sure it's a labeled one, like the ones that came with my pump. No one has ever given me *%&^ about that, but I think they can if they want to...
If you bring a stroller and/or carseat to gate-check on the plane, you will have to fold it up and send it through the x-ray machine. The same is true for a carrier, so if you use a wrap, you will have to unwrap it and carry the baby through, then re-wrap after security.
If you use formula or plan to bring some as a back-up, you will have to buy bottled water in the airport for mixing. They won't let you carry it on, unless the formula is pre-mixed.
I ALWAYS travel with saline nose drops (and nasal aspirator), Baby Orajel, and baby Tylenol, as well as a small vial of Vaseline and a rectal thermometer. The liquid/gel items all have to go in your quart-sized liquids bag, if you choose to take them.
ON THE PLANE
When you hand over your boarding passes, make sure that you stack them so that the person the baby is linked to gets scanned first, followed immediately by the baby. Otherwise, it sets off a little alarm and they have to re-scan your tickets in the right order (minor issue, but you don't want to tick off the other passengers in line BEFORE you get on the plane, LOL!).
I tried my best to postpone nursing until we actually pushed back from the gate and started toward the runway, because DD1 did not consistently take a pacifier. Sometimes this meant splitting a feeding so that I could top her off while we were actually taking off. It worked great, though!
If you bring a carrier/wrap (which I HIGHLY recommend), "technically" the baby is NOT permitted to be in the wrap during take-off and landing. Whether you are asked to remove it will be entirely up to the flight attendants.
Only some airplanes have changing tables, and they are crazy small! Also, I must say that the changing tables on airplanes and in airports are some of the "yuckier" ones I have seen, so I usually bring puppy pads to use and throw away instead of my usual re-usable changing pad. This also means that you don't have to worry if he has an accident on the pad! Oh, and bring a few plastic shopping bags for poopy diapers... even though breastmilk poop doesn't smell THAT bad, it's a nice thought for your fellow travelers

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If you are flying Southwest and they have extra seats on the plane, they will issue your baby a boarding pass at the gate if you have the infant car seat, so I'd plan to gate-check the car seat so you have it just in case! Almost all car seats now are technically FAA approved for flying, but the flight attendant may still ask to see the label. It should be written IN RED somewhere on the car seat, but I'd locate that before you get on the plane so you can point it out quickly if you're asked.
Finally, should a change in pressure occur during the flight, oxygen masks will drop down from above. Pull the mask toward you to begin the flow of oxygen, then place it over your nose and mouth and tighten with the straps. Although the bag does not inflate, oxygen will flow to the mask. Remember to secure your mask before assisting others!