Depends on age of baby. I flew with Malaysian when DS was 4 1/2 months. They were fabulous. So helpful in every way. However all they have is a bassinet, and once he had outgrown that, he then had to be on my lap.
However, British Airways have a pull down tray/table on which they can place either a bassinet or a sky cot. The sky cot will take up to a 3 year old in it. But you need to do this through a travel agent and make sure it is a British Airways plane. They code share with Qantas, and the Qantas planes DO NOT have the sky cot, only the bassinets.
Ask for things like a pram not being included in your luggage allowance, etc. Make the travel agent ring, check what you are allowed to take with you, and GET IT IN WRITING!!! The staff at the airports don't always know what you have been given permission to take with you within the cost of the tickets and I have had several incidents where I have had to get really bolshy with the staff both in London and in Australia. Dont' believe them if they tell you nappies will be supplied, they are cheap plastic ones, and they only give you a couple.
Also, if you can avoid it, try not to have your pram taken off the plane in the stopover for you to use. Although useful (especially if travelling alone), more often than not it leads to you losing the pram, and then having it arrive a day or so later. You can't have it taken off on any domestic connections, anyway, and it has to be checked in in oversize luggage in Australia. Found this out the HARD way - changed the rules when DS was 15 months old!!!! You can always request loan prams at the airports.