I'm a Gambiteer... I'm learning the Blackmar-Diemar Gambit...

The Teichman Variation is another very solid and reliable choice against the BDG.

I think you don't need Nakamura. 

2.Qd3 is of course ok in the sense that white has a playable game, but it's still a bad move, giving away white natural edge without a fight. The question is: is Qd3 going to be an useful move against every possible black setup? The answer is most likely no. Some sample lines:

-2...d5 3.Nc3 g6 (with the idea on harassing the queen with Bf5) 4.e4(otherwise what was the point behind the queen move?) dxe4 5.Nxe4 Nxe4 6.Qxe4 Bg7 7.Nf3 c6 8.Bf4 Bf5 9.Qe2 looks like black is comfortably equal.

-2...d6 with either a philidor or pirc setup must be also very ok for black, Qd3 being a not very useful move.

-2...e6 3.e4 d5 4.e5 with a french defense where again one is hard-pressed to see why white placed the queen on a square where it does little but depriving the LSB of a strong placement.

-ad why not a benoni with 2...c5? i don't recall Qd3 as a part of white usual plans in this line.

The problem with Qd3 so early is that black is not yet committed to a setup where you can say d3 is certainly going to be a good square. Therefore it gives black an easy game. But obviously you can't expect white to be worse at move 2 after moving a central pawn and then playing something with doesn't hang a piece; so yes, it's playable. But harmless.

2 Qd3 is a decent off-beat line against the Dutch, but I don't think it's much good against Nf6, as demonstrated by the previous poster's sample lines.

And to the person who says only 1. e4 is "real chess", perhaps you should try discussing that with Gary Kasparov.

3...c5 looks also good, you're right.

My suggestion is: when you start looking an a "new" move, before calculating variations think about what white idea is. If you can't see why the move should be good(i.e. if you don't see a plan bahind the novelty) you can avoid wasting time on analysis. 2.Qd3 looked dubious for the simple reason that it was really hard to guess what was the plan behind the move. It simply had no sense.

1.d4 Nf6 2.c4 e6 3.Qa4!? I guess the idea is to radically prevent Bb4 and d5. it makes some sense indeed. however i fear an issue might be that d4 is left undefended. Following this as black i would look into a plan putting immediate pressure on d4, such as the straightforward 3...Nc6, attacking the pawn. After 4.Nf3 black can now play 4...d5 (threatening again dxc4-Qxd4). White is presumably forced to 5.cxd5 exd5 to avoid this. We have entered an exchange QGD structure in the wrong circumstances for white, since black will manage to develop the LSB (his main problem in the QGD exchange lines) without trouble. White might instead try to win the bishop pair with 6.Ne5 Bd7 7.Nxd7 Qxd7, but i think black's huge advantage in development should easily compansate for this. I would probably take black here; smells like strategical failure for white, since on move 3 he tryed to prevent d5 and Bb4 at the price of giving black central counterplay, and 4 move later he finds that black has got his counterplay, but also has managed to play d5, and is about to play Bb4 as well!

Maybe a better idea for white is to defend the d pawn more solidly with 4.e3. But white is falling severely behind in development (he has not developed a single piece to black's 2, and it's aven black  to move. A funny idea for black might be to play 4...e5!?, reasoning that black can afford this loss of time since white play has been also very slow. White can't allow black to open the game while ahead in development, so the only move should be 5.d5 Nb8 (probably Nb4 is the same thing) 6.Nc3 Na6 (with the idea of Nc5 to blockade white centre while kicking away the queen) and if 7.e4 Bb4 forces the miserable retreat 8.Qc2 since 8.Bd2? Bxc3 9.Bxc3 Nxe4 10.Bxe5 Qe7 loses. It's just an example which can certainly be improved but black idea seems reasonable, even slow.  Anyway maybe black should just play it simple with  4...d5 5.Nf3 (Nc3 Bb4) Bd7 6.Qc2(sigh...) Be7 and one wonders if black might be not only confortable but slightly better since he is hugely ahead in development. 

On the whole 3.Qa4 reminds me of a statement Nimzowitch made in My system; he said that trying to restrain your opponent possibilityes is an important goal and one of the signs of chess mastery, but sometimes you have to accept that fighting against certain pawn breaks is like trying to stop a rockslide with your bare hands, and just leads to trouble. The plan of stopping d5 here just looks too ambitious, since black can easily support this move. White looks like fighting for an unrealistic goal, and if he is too stubborn in pursuing it he might well end up losing much more that his natural sligth edge.

I know, i just had some fun analyzing it :)