You can't "move" to the Queen's Indian, because you need to play the Nimzo-Indian or something else as your main choice. 1.d4 b6 is not a great opening, though it's playable. Are you happy with the French Defense against 1.e4? Then 1.d4 e6 is the most flexible option; you can enter the Stonewall Dutch, Modern Benoni or Nimzo/QID while avoiding many of the sidelines. There isn't anything flexible about the Slav, and you can't really play the Hedgehog against 1.d4 as far as I understand. Also if you like playing d5-c5 setups, why not the Semi-Tarrasch instead of the Queen's Indian?
Recently, I've realized that I don't have a favorite response to 1.d4....it was the Dutch at some point, but I got tired of ultra sharp sidelines and moved to the QID, but it's never felt like a permanent choice. As a d4 player, I have a rather wide knowledge of black's options from the white perspective, and I've realized that I don't have any necessity to specialize with black.....I can play some flexible first move and transpose.
Between: Nf6, d5, e6, and b6, which is going to be the most likely to get me to positions I'm OK with and avoid ones that might be less comfortable?
I'm OK playing: Main line Slav, QID, Nimzo, Dutch (Leningrad or stonewall), Hedgehog, modern Benoni, and whatever "white with black" lines I can get with d5-c5.