I've travelled short flights (NZ and Pacific Islands) a few times now with Jenna, and what the other say above is all good stuff.
Different staff will treat you differently, I dont know why. For example last time I flew with Qantas they wouldnt let me change Jenna's nappy in the cabin, even though it was only a wet one. Apparently its illegal as its a place where food is served. I had done it several times in the past.... The toilets are really small for a wriggling baby!
Also, some airlines wont let you lie your baby down on a row of seats - apparently again this is illegal. They wont let you have your baby crawling down the aisle either - again illegal!
As you can tell my last flight scared me off a little, specially as I was by myself and got NOOOO help from anyone around me. I even had to ask one of the stewards for a break. They were very rude.

But generally its all OK. Make sure you take heaps of wipes, and small light weight toys. I take a couple of books cause they are good for distraction on take off and landing. Specially as this is the time that all electonic devices have to be put away, so a distraction for that seatbelt stage is great.
Pinch the baby through customs and passport control for usually better service Just kidding - but in all seriousness, sometimes a crying baby will get you attention from the officers, and entry into the quick line!

Have a great time, and enjoy the experience!