We booked for bassinet seat from SQ a couple of times and no issue. Even if baby is in bassinet seat, during air turbulence, take flight and landing, baby needs to be carried out and buckled strap to you. Some parents babywear their baby on flight. My children only slept in the bassinet for midnight flight. No issue but it's also dependent on each individual babies. You can bring along baby's pillow, blanklet or soft toy to make baby comfortable.
Ifbaby has a comfort item I suggest to bring it along. It maybe difficult taking a year old with you. Nevertheless I have friends who he kids and their kids slept through the flight. Take along some toys in case lo get bored. That may help as a distraction IF all else fails.
do you have a baby carrier? I swear by using a baby carrier. Secondly, which airline are you taking? Try to do the online check in yourself so that you are able to see the seats availabilty yourself too.
Baby carrier maybe the answer to your question. That's for worst case scenario. Also get the bassinet. In that way baby can still sleep properly if all goes well.