Interesting forum, I love the Queen's Gambit (I play it a lot) and I always try to play it positionally. You do not need aggressive play, in fact the opening is usually the opposite. Do not be fooled by the name, the Queen's Gambit is not a "true" Gambit. When the opening was created it was thought to be a gambit (as you are clearly sacrificing a pawn), but newer analysis (as of last few hundred years) has shown this to be a solid opening where White can always get the pawn back, or Black is forced into extreme measures that are often unfavorable (pawn not worth the effort, and Black should eventually return the pawn). The Queen's Gambit is a really old opening, therefore with a lot of theory. For example, the Queen's Gambit Central Variation, Greco Variation (d4 d5 c4 dxc4 e4 b5 a4) was played by Greco circa year 1600! Isn't it cool how old chess is, and even computers agree with some of these ancient lines? An opening from the 1600s I still sometimes get over the board over 400 years later! If White learns the theory, this will be seen as not a "true Gambit" where aggressive play is not required (as gambits often require). If you compare this to true gambits such as the King's Gambit, or the Danish Gambit, you will see many differences; Queen's Gambit is, by contemporary views, a misnomer title - as it is not really a gambit upon closer inspection into the vast theory.
I tend to write a lot at times, but as a Queen's Gambit player (and upon noticing your forum question not 100% adequately answered), I feel almost obligated to write this. Usually players mention this opening getting the pawn back by the normal variation (d4 d5 c4 dxc4 e3) but e4 lines are equally rewarding (although more theory is probably needed for 3.e4 versus 3.e3) and the pawn often is still returned (willing or unwillingly). Many knowledgeable chess players recall a line where Black loses the a8 Rook if they attempt to hang onto the pawn (via White's Queen on f3, of course via 3.e3 not 3.e4) - however, getting the pawn returned is much greater than this known trick, as this merely scratches the surface. Gambits usually end up in an inferior position if the opponent knows the opening, but this is not as true for this opening. Obviously opening knowledge is beneficial (even without gambits), but gambits especially crumble against higher level play. This is why the King's Gambit is rarely seen past 2000 rating, or the Englund Gambit past 1600 and so on, but the Queen's Gambit is played even at GM play - it is simply not a "true Gambit".
By the way, on a side note: against the solid London System c5 early on is surprisingly effective with Queenside play (of course study this a bit before a game, but this should get you started) 
In conclusion, aggressive play is not usually coming from the Queen's Gambit (but any opening can of course turn sharp and aggressive very fast) and this opening is actually not really regarded as a "Gambit" at all nowadays. I hope this better answers the deep thoughts here in this forum; this is really just the tip of the iceberg. I do not intend to write a book from this long post, but a lot needs to be addressed and clarified here. I hope this is seen as helpful 
There is also the London System . Works against practically all openings.
d4, Bf4, Nf3, e3, Bd3 (or Be2, which I prefer), O-O, c3, Nbd2, Qc2.
Personally, I'm get very comfortable positions in this opening, and it avoids a lot of theory.
Three common responses by black to be aware of:
1) KID. Try to keep their Bishop blunted with your pawns on c3, d4, e3.
2) When they want to disturb the balance with c5, if they capture, try to recapture with the e-pawn (if tactically possible). This allows for easier development and attacking lines at their king.
3) Be aware. This opening is very strategic, and becoming popular. Don't get lost in crazy tactical lines. Instead, go very smooth and solid, waiting for your opponent to make positional errors, then pounce.
Studying endgame positions by Capablanca will help you to understand how and when to capture .