I have an 8 week old baby and she flew to San Diego and did really well. She slept through take-off and landing. I really really really recommend using a sling. They feel really good on your back and babies just love them. Don't sit at the bulkhead or very back because you're definitely going to want a seat that sits back if the baby is going to be in your lap.
We're headed to Australia in August and she will be 3 months old. Most international airlines will have seats w/ bassinets, but its really a first come first serve basis. So once you book your tickets you're going to want to call the airline and request a seat that accomodates a bassinet. Otherwise, you might not get that nice FA or have someone who doesn't want to switch seats.... or other people w/ infants took them.
If you're a frequent traveler, as we are, its really a breeze. If you're not it may be a bit of work.
What's interesting is she has her passport and you have to put their height and eye color and hair color as it is now and they don't expire for 5 yrs. So our daughter will be traveling when she's four or five and her passport says she has brown hair, blue eyes and is 23" tall.
Good luck... do it while they're young or you'll probably regret you didn't