q and -q represent the same rotation, unit quaternions are a double cover for the sphere.
The only issue is when interpolating/slerping quaternions, you want to go the quickest route rather than the long way round, but you can do that by checking that the quaternion dot product between the 2 quaternions is positive, if it is negative negate one of the quaternions before interpolation.
EDIT: If you think about the axis/rotation form of a quaternion it is easy to see that -q and q represent the same rotation; the axis is negated but so is the rotation angle => they represent the same rotation.
EDIT2: Euler angle representations aren't unique either, so converting Euler angles to a quaternion and then back again might not give you the same angles back either ;)
EDIT3: So in conclusion, there's nothing to worry about.