Long-haul flights with Baby

OPTION 1: TAKING BUGGIES ONBOARD

Call/email your airline weeks ahead to find out their policies regarding buggies onboard.

Tell them at check-in that you want to hand the buggy in at the gate. 

At security they will definitely want to dismantle and scan the buggy so you'll have to take your baby out and carry him/her through the metal detector. 

Then strap baby in again for the long trek to the boarding gate. 

At the boarding gate try to find a helpful steward and ask him to put the buggy somewhere where they can retrieve it easily when you land so you get it at the gate. This, I believe, is only a problem on Qantas where the large number of Buggies onboard have recently meant a lot of Moms having to stow theirs with the luggage. Which means, not only will you walk miles to baggage reclaim but risk the buggy getting battered (hence no longer as safe as the manufacturer guaranteed)

OPTION 2: BABY CARRIER
Take bushbaby sling to carry baby in. 

This is a good idea if your baby is younger than 4 months and the added warmth and closeness might help him/her sleep calmly through.

Otherwise, remember this will limit how much cabin baggage etc you'll be able to carry.

In my experience, you won't need a baby carrier, if you manage to take your buggy onboard.

TRAVELING ALONE WITH A BABY
Generally most airlines are helpful. Tell them you are travelling on your own with a young baby and they will arrange assistance both ends. According to Mumsnet.com's forum users, the Best airline for travelling alone with Babies is Singapore Airlines and the Worst is Qantas (not my opinion, folks).

TAKE-OFF and LANDING
Make sure to feed baby during these to prevent inner ear pressure change pain. For babies older than 4 months, or when they're able to sit up on your lap and hold their head up, you could use the seatbelt extension. With baby lying sideways (facing you) on your lap you could feed her (under cover of a shawl or scarf) through the take-off and landing bits. Or you could bottle feed. A dummy/soother/pacifier doesn't have the same effect.