Harley had been independent at one point in the comics. She had her own series in 2006 (or around there) where she ran her own gang by herself. It...wasn't bad, per say, but it didn't feel quite right either: the series added things to her mythology that didn't make much sense and aren't brought up outside of the series. And yes, whenever the Joker kicks her out she usually goes to Ivy, but even in the animated universe there have been points where she's reformed (never lasted) and lived on her own. So she could manage if she really committed to it, but she generally prefers being in a more submissive, codependent role. It probably has to do with the lack of parental guidance she had during her childhood as well has her whole psychosis in general.