We plan on HS, but nothing "official" until DD is 6. She'll just turn five when the babe is born, so I'll need a few things for her, but nothing too serious. Right now, we're focusing on beautiful things-- music appreciation, art appreciation, and character development. These activities are very open-ended requiring minimal introduction. We listen to lots of Classical Kids CDs, and that can be done while you nurse/care for your newborn.
In addition to re-structuring your schedule a bit, I have these ideas to toss out:
I don't know what kind of program/curriculum you prefer, but we love the Beautiful Feet literature packages. DD already has me read them to her, especially Abraham Lincoln. So, we sing songs about Abe, check out books about Abe from the library, build log cabins from blocks, etc... Is there something your DD really LOVES that you can expand on using literature, arts, and math skills? For example, if she is obsessed with ponies-- she can build complex stable arrangements, listen to Black Beauty via audiobook, etc..? When I was teaching, I also had my students write and maintain their own "National Geographic" journals where they journaled their science lessons, topics of interest, etc...
And caring for a newborn is an education in itself! We love the character training/devotional by Clay Clarkson called Our 24 Family Ways. We read/discuss every morning over breakfast. Your DD can apply what she is learning, say about caring for others in the home, by pouring juice for the family, or loading the dishwasher. She could learn and pratice great homekeeping skills as well as the character of servanthood (age app. obviously).
I find the Montessori principles of teaching young ones to do it for themselves to be so helpful. Maybe that can be an avenue as well.
Sorry for the novel--this very topic was on my mind as well and it looks like I did my thinking via typing.