2... Qf6, while not strictly unsound, is definitely an inferior move, not only because it develops the queen prematurely, but also (and more importantly) because it deprives the black king's knight of a very natural square on f6. Don't panic about a possible king-side attack -- black cannot mate with no minor pieces developed. There are a number of reasonable continuations for white:
3. Nc3, a natural and flexible developing move that eyes the d5 square, threatens to chase the queen with gain of time, and doesn't commit to any particular pawn structure.
3. d3, a perfectly valid move, but somewhat passive and has the distinct flaw of locking in the light-square bishop. Unless you strongly prefer to play slow, positional chess, I would develop with
3. Bc4 prior to playing
d3 (if at all). If you play
d3, the logical plans are either to prepare a central break with
c3 and a subsequent
d4, or to castle kingside and prepare
f4 after re-maneuvering the f3 knight. Which of those plans is preferable depends on your opponent's development, of course.
3. Bc4, versatile and potentially very aggressive, threatening an eventual
Ng5 and pressure on f7 after white's d-pawn moves. This is definitely the move I'd favor in a rapid game, and I don't think it's objectively worse than
Other moves, such as
3. d4 and
3. c3, are probably sub-optimal. An immediate
3. d4 push is likely to lead to exchanges and a relatively drawish position (and might end up transposing to lines of the Scotch that are not particularly good for white), while
3. c3 is slow and somewhat crude and might allow black to equalize with dynamic piece play.