Problem 2 , month 1. Alternative solution?

The solution was to exchange queens, which leads to a won endgame. But I found 1. Qd4 which wins tactically, taking advantage of the pinned rook. if black plays 1...Qd3, then 2. Qa1 wins. I think this should have been mentioned. i know that GM's prefer a sure endgame win to a flashier tactical win, but still...
Can anyone refute my analysis?
Thanks in advance.
If you want to use an engine, copy and paste the following into your game window.

[Event "?"]
[Site "?"]
[Date "Mar 4, 2010"]
[Round "?"]
[White ""]
[Black ""]
[Result "*"]
[DisplayPlyCount "15"]
[FEN "8/5p2/b2p1k2/Pq2r1pp/8/4P1PP/1Q3PB1/2R3K1 w - -"]

1. Qd4 g4 2. Rc6 Kg7 3. Rxd6 gxh3 4. Bxh3 Qxa5 5. f4 Qe1+ 6. Kh2 Qxe3 7. Qxe5+
Qxe5 8. fxe5

I also found Qd4 but I have to say that the given solution is much better under a practical point of view. After four hours the player could be tired, I know I will, then to miscalculate is very likely and why would white get into complications if this only would give black chances to save the game?

Yes, avoid complications when ahead is my motto!

But good eye.