Yes, Sinoflyer is indeed correct. I once arrived close to midnight and then needed to connect to Druk Air at like 6 or 7 am. The problem was that I needed to wait for their transfer desk to open. So I hung out in a pay lounge (they take Priority Pass) and then around 4 am I headed to the Air France lounge.
I would definitely grab a hotel for this itin. There is an airside hotel that seems crappy and expensive for what it is. There is also a Novotel at the terminal. It's decent; stayed there once.
But I would head downtown. The cab ride will be fast at night and cheap.