How would you handle this opening?

I've come across this opening several times and I don't have a gameplan for it.

What would be a good way to handle this as white?

I don't find this one especially threatening...

Basically black is just opening the queen up...

I'd keep developing...

Nc3    c6

d4    exd4

e5    Qg6

Qxd4  Na6

Bxa6  Qxg2

Rg1

It's Greco(something) defense

Laugh at him, get up and walk away.
then tell him to come back if he knows how to play chess...
that or Nc3

I think most chess players look at that opening and go, oh, that's a beginner opening... and it is, generally, but it isn't "losing" -- there's no tactical refutation or any forcing moves for White that establish a solid winning advantage. White shouldn't get over confident.  Normally when the queen comes out early like that you want to attack it, but in this case the queen is taking away the natural development square from his N without accomplishing much, so proceed with do what you normally do (take center and develop pieces) and the defects in his opening (exposed queen, loss of tempo, awkward N development) will cost him down the road, we hope.

But this opening is really old. And the masters of yesteryear were fond of bashing folks who played it!

Here's some ultra-miniatures Greco vs. Patzer (all based on a simple trap wouldn't expect any but very low-rated players nowdays to fall for), and a 23 move attacking firestorm in Morphy vs McConnell ... all in one convenient diagram... just go to the move list and click thru the variations.

Since 1620, this is known to be a poor opening for black:

Nothing changed ever since: