Basically, you’re going at a great time - I think a six month old shouldn’t be too much of a problem, as she’ll sleep a fair bit. IMO flying with a child between one and three would be living hell, but I’ve never attempted that 
I think it’s great that you’re buying an extra seat (we never did) but be warned - it will be expensive. I think industry standard is something like 50-80% of full fare for own seat. Something lke 10% for ‘on the lap’. If you’re going to pay for a seat, you might as well bring a car seat. Many of them can be used on airplanes.
Try as if your life depended on it to book the bassinet seats. Book early, and nag them. Coming to Taipei, I made several calls and reminded them every single chance I got that we needed the bassinet seats. These are the best, particularly if you fly economy, because they attach to the bulkhead, so in addition to the cot, you’ll have heaps of extra leg room and space for the sherpa-load of stuff you’ll be taking 
Take off and landing - as rubykate says, you’ll get an ‘extension’ seatbelt, unless you use the carseat, of course. (The bassinets cannot be installed until the plane is in level flight.) Funnily enough, these are actually those little strips of seatbelt they use for the safety demonstrations. Breastfeed or bottlefeed during takeoff and landing and all should be well. The extension seatbelt is definitely less safe than a separate car seat, but the odds are greatly in your favour anyway. During turbulence you may be asked to remove your baby from the bassinet, even though it does have safety straps.
If it’s a day flight you’ll need more than a night flight, but basically bring everything you’d take for an overnight trip. Spare clothes and bibs are vitally important. Bring water in a bottle for you and baby - the planes are incredibly dehydrating even on adults. You may receive a baby bag with nappies, disposable bibs, baby food etc, but it’s always best to bring everything you need, just in case. If you bring a bottle you can ask the stewardess to warm it for you - CHECK THE TEMPERATURE if you do, obviously (I’ve never done this but I know this can be requested). Good luck!
Oh, and change facilities are available in the toilets - if you think airplane bathrooms are squishy, think of the fun you’ll have changing her in one 