[Dounia:] "Trust me in this matter and, believe me, I shall be capable of judging impartially." (4.2.69)
We believe you, Dounia! She wasn't quite so impartial when judging Svidrigaïlov and it got her in a heap of trouble, but she gives Luzhin every chance to pretend to be a decent guy before she kicks him to the curb.
[Dounia:] "Pyotr Petrovitch [Luzhin] makes no secret of the fact that he had a cheap education, he is proud indeed of having made his own way." (3.3.124)
Did you find it odd that Dounia has a better education than Luzhin, yet she can't get a decent job and he can? This is because very few professional positions were open to women in Russia (and elsewhere) in the 1860s.