Not only do I advocate for having a backpack diaper bag in general, but it's essential for traveling. Even with baby, you'll be hands-free, and pockets galore mean you'll stay organized. Plan on only having this as your carry-on (even though you're allowed two — trust me, you want to be able to be as hands-free as possible).
Once you've put your baby in the carrier, then you sling your diaper bag on your back, and you are literally good to go. Pack that sucker full of the essentials you'll need, and stash your cell phone, wallet, and anything else you need access to in the front pocket. When you have to check in and go through security, they'll be easily accessible. I have this backpack from Skip Hop ($80), and I can't say enough good things about it.
Sub-tip: Put a slim, foldable diaper clutch (like this one from Herschel, $30) in the backpack, so when you need to perform a diaper change, you can pull that out, hang your backpack on a hook, and change baby without going into the whole bag.