You are on the other side of the river, but you also have a bridge next to the hotel, which will be empty, so I wouldn't worry about it.
You can get a car door to door. I presume you are booking everything DIY? If so, I can't advise an alternative to the hotel, who will slightly overcharge you (but probably pennies considering it is Thailand!).
I presumed you were getting an internal flight - but I guess not if you're flying Qatar. You won't like what I say, but i'm so ultra cautious, can't stand rushing before a flight, or risking road delays etc, or a breakdown, I am always at an airport 3 hours before an international flight.
It keeps me less stressed, even if I do have to get up early! But everyone is different. For the same journey, i'd be leaving at about 4.30am! I'm sure others will say that's completely unneccesary