I've never flown economy on Qatar, I always fly the Q Suite out of JFK. They have asked me for onward travel every time. Even my explanation that I was going to drive from KL into Singapore wasn't sufficient. They made me book a flight on the spot before they would proceed with the check-in.
Qatar absolutely will not let you board without proof of onward travel. That was the case even pre-covid. Other airlines aren't as strict but I'd say have something booked anyway just to be safe.
I'm not aware of any public health agency that recommends pre-exposure rabies vaccine for people that are having episodic exposure. If you're going to be around tons of wild animals on a daily basis, yeah by all means get it. If not, the concensus seems to be its rather unnecessary if you're in a developed country like Thailand.
They instructed me to leave my suitcases off the xray and only place my backpack on. Nobody was looking at the screen when it passed through anyway so not even sure why I needed to do that 😅
Make sure your covid test specifies RT-PCR. I had friends get denied boarding by Qatar even though their tests were RT-PCR just because it didn't specify that on their printout.