Yes. Donna is smart and she's not afraid to use her intelligence and let it be seen, and travelling with the Doctor lets her do that in a way that her life on Earth didn't. It's an interesting inversion of what happened with Rose and Martha - they learned from travelling with the Doctor that they had resources they'd never imagined and they could make their lives as good as they wanted them to be, but Donna already knows that and hunting down the Doctor is her way of making that better life happen. I'm not sure how much more I can say without being vaguely spoilery, but the difference between the Doctor with Donna and the Doctor with Rose and Martha is striking because Donna is so different from them in so many ways.