I think you mean you prefer the QID over the QGD :-) Also, the Catalan is immensely popular at top level, so it's probably not that bad. You need something against the Catalan anyway because of 1.d4 Nf6 2.c4 e6 3.g3.
You could go for 1.Nf3 Nf6 2.c4 b6. There are independent lines like 3.g3, but all in all I think that stays close to your preferred QID, and of course it transposes as soon as white plays d4.
Ok,
So If d4 I play Nf6, if c4 then e6, then if Nc3 Bb4 and if Nf3 the QID with b6.
What if they start 1. Nf3? Well, 1...Nf6 is still the way to go, to guard e4. Then 2. d4 transposes, but 2. c4 keeps it sneaky. After 2. c4, I don't want to play 2...g6, and 2...c5 is also not the QID. So I play 2...e6 aiming for the QID or something related. If they play 3. g3, I can play 3...d5 and they are playing a Catalan, which isn't whites best way to play d4 openings. If they play 3. d4, I can play 3...b6 with my favorite QID.
But what if they play 3. Nc3? In other words, 1. Nf3 Nf6 2. c4 e6 3. Nc3.
If I play 3...d5, it is a QGD, and since the QID is prefered over the QGD, that would mean that 1. Nf3 was BETTER than 1. d4, since blacks best (QGD) would be not as good (as QID).
The next most popular option on the database is 3...Bb4. But it didn't seem like a very good move.
What to do?