I think you should be careful with bring liquor bottles through Doha. The first thing you do when arriving at the Premium Terminal in Doha is going through a security check. I cannot say for sure whether or not they'll allow you large bottles to go through.
Security checks at the Premium terminal seem fairly relaxed. I never had a problem on the flights I had, but that does not mean that it's always like that. The last time I flew through to Doha was January, so things could have changed since then.

There is a duty free shop in the premium terminal, which sells booze as well. The selection is limited but I would think a brand as popular as Bailey's should be available. I can't tell you how prices compare for Doha vs LHR duty free, but I would think that even if the booze is a bit more expensive in Doha, it'll be cheaper to buy just once there, rather than taking the risk of having to buy again after your bottles were confiscated.

Your last resort is also the duty free on arrival in Bangkok. Again, I am not sure how prices compare.

As for the upgrades, I seem to remember having read here that QR don't allow standby upgrades from C to F. They will insist on re-issuing the ticket rather than allowing a one segment upgrade. I have tried to purchase upgrades from C to F twice (both in Doha - once to Paris and once to LHR) but was told both times that they can only do this by reissuing the ticket.

I agree with the previous reply though, the business class on their 777-300 is awesome. Enjoy the flight