Black has a small advantage in your position, but it's certainly not unplayable for white. Stockfish rates the position you've given around -0.2, which is pretty close to even. If black plays well it seems difficult for white to get a good d4 break, though if black tries too hard to chase the queen perhaps white will be able to get back the advantage. The main problem seems to be that the pawn on c3 is counterproductive: white can't play d4 with advantage and the pawn on c3 interferes with white's queenside development.
Stockfish suggests the following line, where black retains a small advantage (around -0.3)
1.e4 c5 2.c3 d5 3.Nf3 dxe4 4.Qa4+ Bd7 5. Qxe4 Bc6 6. Qf4 e6 7.Na3 Bd6 8.Qg4 Ne7 9.Nc4 O-O 10.Nxd6 Qxd6 11.Be2 e5 12.d3 Nd7 13.O-O Rfe8
Black is somewhat better off playing Nc6 on the 4th or 5th moves instead of occupying that square with the bishop. White is still fine, but should avoid 4. ... Nc6 5. Qxe5 and instead play 5. Ne5.
1.e4 c5 2.c3 d5 3.Nf3 dxe4 4.Qa4+ Nc6 5.Ne5 (5.Qxe4 Nf6 6.Qc2 a6 7.d3 e5 8.Nbd2 Be7 9.Nc4 Qc7 10.Be2 O-O 11.O-O Nd5 ) Bd7 6.Nxd7 Qxd7 7.Qxe4 Nf6 8.Qf3 e6