I've got twins and regularly fly QR with them. Bare in mind that they will only just fit in the bassinets in February - and if they're crawling by then (they will be 6 months old then, right? So they might be almost crawling) then you might not have much luck getting them to stay in the bassinets! But you should be OK at that age. I found it was from 8 months onwards that flights started to get 'challenging'.
I've also found that you need to nag everyone you meet from QR, starting with going into an office now, and talking to check-in, and then at the gate and then on board, to make sure those bassinets are definitely yours. Don't assume that because one person has said yes, that it has filtered down. Keep nagging and you'll be fine, but if you think you've booked them and then relax, that's when you can get a nasty surprise on the day.
As for a golf cart at DOH, you're not supposed to have access to them, but on our last flight out in August we managed to flag one down and persuade him to take us down to our gate, which was all the way down in E. He told us he wasn't supposed to do it though. I don't know how we would have managed it otherwise.
But at 10 months I presume you will have a stroller with you anyway? (I would definitely take one if you can). And if not, there are plenty available at HIA.
There is meant to be a train opening soon at HIA, but I have heard from someone very senior at the airport that they are having huge issues with it, so I wouldn't bank on it being available by then.