Correct. T1/2/3 are all joined, either walkable or by skytrain. The new T4 is separate.
Should be able to go to either. QF lounge is larger and has better food, though can be busy. BA lounge for real champagne if that's important.
And in Doha you want the Al Mourjan lounge (not the oneworld business lounge). It's a somewhat strange layout but best food is up the grand staircase, although the sandwich Bar on the opposite side is also good.