Bringing out the queen early is bad only if it can be attacked. Here're some examples:
1. e4 d5 2. exd5 Qxd5 3. Nc3 Qe5+? 4. Be2 Nf6 5. Nf3 Qf5? 6. O-O
Black's position is a wreck because White has managed to develop with tempo two times (3. Nc3 and 5. Nf3), and is threatening to do it yet again (with an eventual d4-Bd3, gaining time yet again while opening the e-file for the f1-rook). These moves are "free" because while White is developing pieces, Black has to respond to the attack on the queen. This is why the standard move in this opening is 3...Qa5, which places the queen on a square which cannot be easily attacked.
However if the opponent cannot attack the queen, it's perfectly fine to bring out the queen early.
1. e4 e5 2. Nf3 Nc6 3. d4 exd4 4. Nxd4 Nxd4? 5. Qxd4
In this line of the Scotch, okay, now White's queen is in the center, but Black can't attack it. If Black could still play ...Nc6, then yes, the queen is vulnerable, but the knight isn't there anymore. Black could play ...c5, but that permanently weakens the d5-square and after White moves the queen, Bc4 and Nc3 would turn Black's "gain of time" into seppuku.
Another, more sophisticated example:
1. e4 c5 2. Nf3 e6 3. d4 cxd4 4. Nxd4 Nc6 5. Nc3 Qc7
Once again Black has developed his queen early, but White has no good way to attack it. Playing Ndb5 or Ncb5 doesn't gain much time because the knights are already developed, and Black will regain the tempo eventually with ...a6. If White could play Bf4, then 5...Qc7 would be bad, but the line 6. Ndb5 Qb8 7. g3 (forcing Bf4) a6 8. Bf4? e5 would lose White a piece.
Conclusion: in the opening, feel free to develop your queen where it's active as long as it cannot be easily attacked. If the opponent pieces can leap into battle by attacking the queen, don't do it. If they can't, by all means.