I have a 2004 3.0Q tip and I have a similar problem when moving. Rolling in traffic, then giving it a sudden 1/2 to 3/4 throttle leaves the car confused for a second, as if its like "really? You want to go, NOW? Alright, I'll pick up my shit,"
Whats worse, is that this soggy response contrasts SHARPLY with the strange behavior from a dead stop: it actually lurches/lunges forward for an instant at tip in. Even with a smooth & fairly slow application of throttle, it feels as if the throttle is momentarilly 'goosed' open, causing the car to jump forward. It may sound great in comparison to the lag, but its really noticeable in heavy traffic and very tiresome to have your neck snapped around, particularly for passengers. Plus, the uninitiated think the driver is a ham-fisted retard.
Personally, I think the problem is a combination of several things:
1) Wacky DBW tuning where it is not 1:1 in certain situations. Probably set up to make the car feel more powerful than it is for the unwashed masses. The dead spots where the response is soggy are probably the easy way out for emissions testing. Its monkey business that reminds me of the 1979-1984 Eldorados with the 4100 motors: they had a much shorter than normal pedal travel--it fooled people into thinking the car was stronger than it was (until they went to floor it & realized they were almost there already).
2) Clumsy shift mapping. There is some wacky shift strategies going on in there, and the no time in 1st is a direct result of this. I noticed it in the Q7 loaner we had last time--very annoying because the 1-2 shift actually takes LONGER than the time it spends in 1st gear. On my own car, I also notice in many situations the trans shifts too soon/too late. I wish there was an aftermarket software that cracked the maps, I'd love to try my hand at enhancing them. Fortunately, at least we can switch around between several 'pre-fabbed' strategies with the VAG com; still waiting for my cable.
Guys, next time you drive your car try to duplicate the situation that causes the hesitation, but before getting on it, flick the shifter into tip mode. Odds are, you are in 2nd, and when you gas it the trans goes down to 1st, then back into 2nd. Putting it into tip mode will (at least on my B6) keep the trans in 2nd, instead of wasting time shifting down to 1st only to almost immediately shift into 2nd actually spending more time shifting than going in the first couple seconds. If putting it in tip mode makes it go away, its simply the shift strategy.
3) Lazy shifts. Great for the unwashed masses, since most just want a smooth ride. Why they didn't tune it to have smooth shifts at lesser throttle applications, and have higher line pressures/firmer & faster shifts at higher throttle applications is beyond me (and yes, it is possible to do that). Here again I'd love to get the transmission manual & look into how it regulates line pressures, and which accumulators correspond with which shifts, etc & do my own R&D on a home shift kit but IIRC the manual is some $800, with no guarantee of result. Still thinking about that one, but odds are it won't happen.
Couple a lazy DBW setup with a lazy shift & a shift strategy that doesn't know whether its coming or going, and, well, we all know the outcome. Personally, I'll be happy if I can just get rid of the damn 'lunge.'