As I’ve mentioned in a previous post, caring for ghost-types is actually relatively easy, anonymous. Most of them only need a bit of food, water, a place to relieve themselves, and little else. Duskull especially are among the most docile of ghost-types and rarely even need a vigilant eye (as they don’t typically engage in excessive pranking). Yours may be even easier than that, as she was eager to become one of your partners.
Thus, all I can offer is a short word of warning: duskull dislike light, more so than a lot of other ghost-types. You’ve probably already realized this through observations of the strange activity in your home. However, the point is, try to give her a cool, dark place to rest if she hasn’t already chosen a part of your home as her own corner already.
Best of luck, anonymous!