Firstly probably impossible to say for sure when your arrival at airport would be unless staying near airport. Consider traffic at such a time ,extremely optimistic
Depending on which country you come from nearly all international flights land at BKK .DMK is more for domestic and budget airlines so more often than not you have no choice. If China visa office is in same location as Embassy then both airports are a similar distance .Once you establish that use a hotel site such as Agoda to see what suits you .
Be aware of the hurdles you may have to jump returning to your home country SHOULD that be the case .The cost to bring the dog to Thailand may in itself be more than your plane ticket for yourself. Obviously the value that you place on your dog may well be infinite.