I can see both sides. Professionally, I don't think asking about childcare costs will go down well. As others have said, it's this sort of thing that could potentially put employers off hiring women of child-bearing age. Yes, it's wrong - but it is what it is.
Financially, though, as you say, a company would naturally pay for flight, hotels, meals etc on the basis that, if you were not in Africa, these are costs you wouldn't incur. So, by that same logic, if you were here and not in Africa, you wouldn't incur the costs involved in having to pay someone else look after your child. So, for that reason, it should be factored in like any other expenses.
All that being said, if I were in this scenario at work, I'd probably want to demonstrate to my employers a willingness to travel and would suck up the cost.