That's right, education doesn't stop at 3.15. When you are home educating, you'll be educating from waking til sleeping!
I well remember getting 'cosy' with my hubby late one night, when dd2 came in and "Tell me about polysaccharides........." 
It won't matter a jot really when you work really, as long as you make time to give your child what she needs from you as a her facilitator of education.
It may well be that your child will be getting on with something, whist you are making calls. There will be times when she is so absorbed in some
I used to arrange to take work calls when our children were happily occupied at HE activities.
I have taken work with me to home ed camps (at Peak Camp you'd often find me up the lane taking calls where I could get a signal!)
Almost all home educators I know, do so on a limited budget, a large number of them are either in a partnership, where they both have to bring in some sort of uncome or both work part time-or they are single parents who have to work some hours.
Home educated children, get to see how things are in the real world, they learn the realities of working to bring in money, in a very direct way.
I think with what you have described, with support from your family, you'll easily be able to offer your child an suitable and efficient education.
I can't remember the source, but studies have shown that a child at school -far from coming first-gets about 18 mins one to one time per week!
Even if you choose to do 'lessons/school at home' type of HE, it is SO much more efficient than school, you'll easily cover in a couple of hours, what would take all day in school!