No need to panic with 7... Qd6, just play 7... Be7. Black is perfectly fine.
Caro-Kann with early queen attack

See my analysed games in the thread below.
There is a lot of games I won easily just because I could pressure the opponent after his attack with the early queen.
Did you look at 6. Bg4 to attack the queen and get your bishop outside your soon to be center pawn chain? and 7. Be7 should be automatic for you (opening principles!)-breaks the pin, develops a piece, prepares to castle, and over protects your f6 square allowing for your queen to move elsewhere whenever you want. This is a good minature that highlights how opening principles can help you avoid tactical shots even if you don't see them!

Yes e6 isn't a very caro-kann move, and bg4 insead is a free move, that shows qf3 up as not a great move.

Yeah, 6...Bg4, Queen moves, likely to a dark square, and then 7...e6. If White plays anything other than 8.Bg5, you play 8...Bd6. If he does play 8.Bg5, you have to take care of the threat of 9.Bxf6 and 10.Qxg4, but so what? Just go 8...Bf5, attacking c2, protecting the Bishop, and preparing to unpin the Knight with 9...Be7, unless White trades, in which case you have the Bishop pair in a Semi-Open position.
Dear chessers,
I have started to learn the CK lately and came under massive pressure due to an early attack with the queen and the bishops. Could you tell me what I could have done better ?