Unless she's living with her grandparents.
I see it like this: Dexter loved Rita and the kids, but seeing Arthur's relationship with his family jolted him and made him wonder if he would be bad for them in the long run. Rita's death clearly proved that he was, in fact, bad for Rita, at least. Now he's stuck with the task of raising her children, which he might be able to do; but realistically the best thing for them would probably be to have them live with their grandparents. Dexter's not exactly that attentive, plus he accidentally got Cody to lie for him, plus he's never understood Astor or her adolescence, plus he's going to be out a lot murdering people rather than being there for them, etc. I know there's been some debate about how Dexter wound up having to take care of the baby so much, but Rita undoubtedly did the lion's share of the work with Astor and Cody. So if they live with their grandparents, they're taken care of, loved, and generally raised better than anything Dexter could provide.
Harrison, on the other hand, has been "born in blood," just like Dexter. So Dexter is pretty much the only one who can properly raise Harrison, if indeed he has a Dark Passenger of his own. I think that's a good compromise of leaving Dexter with a lot of increased responsibility without necessarily overwhelming him or making him sloppy.