I don't think the QID setup is especially good against the London. Kasparov and others have played a plan with a4, then Nd2-c4 with an edge for white. At least as much an edge as can get with London against anything anyway.
If don't mind the french, Eingorn as suggested 1.d4 e6 2.Bf4 c5 then early Qb6 which looks very sound.
Some time ago attempted to play the Nimzo/ Queens Indian combo myself.The consensus on this forum is that it is the perfect black defense. However there are some problems. Firstly it is a tremendous amount of work, covering in addition catalan, and non c4 openings like the london.
In addition the QP openings, like the london, have more kick against an early e6, than for example d5, where black equalises smoothly with minimal effort, or the kingsindian were black has more flexibility, and greater winning chances.
Another problem is that the Queen's Indian itself in many lines leads to some of the dullest and most drawish positions in chess.
These issues lead me to decide to take up the KingsIndian instead.
I've played the Dutch so much that I might as well get a t-shirt that reads "1...f5!!", but, as I improve, I'm beginning to get the distinct impression that my opponents are going to eventually stop conceding me the whole center, the bishop pair, and a massive attack in every game. So I'm beginning work on a QID/Nimzo repertoire, and, as a d4-c4 player, I'm relatively confident in meeting most of the main line stuff since I know the structural themes from the white side, but the London always puts me a little bit on the back foot.
It's not that 1.d4 Nf6 2.Bf4 d5 is incredibly good for white, it's that we're playing exactly what white wants us to play. The London player is a humble sort; they don't want an opening advantage, they want a pawn in the center, a good bishop, and a position that they understand and feel comfortable in....like an old sweater. Being the contrary sort of woman I am, my repertoire goal is to forcibly drag the position away from what Mr. London is trying to achieve, and I want to get there without sacrificing pawns or making goofy looking, unsound moves.
After playing around on my own with an engine and then comparing that with a database, I came up with a sort of theoretical main line which I'll add below, but I thought it might be helpful to pass the question along to the forum: What sorts of nontraditional setups work against the London? How are others peeling white out of the comfort zone after 1...Nf6 2.Bf4?