The point is, white may have space and a tempo for development, but he has to turn that into something real. That is not an easy task. Seriously, imagine pawns on e6 and c6 for black, putting max restraint on d5. You have to come up with a concrete plan to break through that. Sometimes, white actually plays d4-d5 anyway, even with pawns on c6 and e6, for tactical reasons. But again, these kinds of breakthroughs demand much creativity on white's part.
Of course, this is assuming black plays very well. Practically speaking, black will be punished more greatly for his errors than white. I'm just saying that objectively, black's position is not necessarily doomed to fall apart, even if it may look that way.
I'm not even sure if ...Qd8 is so much worse than ...Qa5, given that the queen on a5 will probably need to find a retreat square soon enough, as it is bound to get chased again. It's not like there is anything so special about the queen on a5.
It's hard to play a terrible move so early on, but it has a good go.