It was 100% not there at the start I remember it coming very well as I liked it at the time (I was at college and very lazy, so it meant I could smash out tonnes of random heroics instead of running around Dalaran waiting for something to happen when my friends weren't on). Otherwise nobody really did dungeons by the time it came out as they were a piece of piss and dropped nothing relevant.
Initially there was a tool where you could see other groups, and whisper the leader but IIRC there was no 'apply' button, so it was a lot more similar to the non-teleporty LFG system we have today. The teleporting to dungeon was later, either the ICC patch or perhaps the ToTC one and didn't apply to raids until LFR which I think was Dragon Soul.
Edit: Final point, I don't think I'd like the teleport-LFG tool, I don't think it chimes with the experience I had playing classic which I really enjoyed, they may add it, but I don't think they were targeting 'player minutes' in the same way back then, and so perhaps not.....