Sorry, Mintyy, I read your post as saying 'If I were your nanny', but I see you said 'If I were a nanny'.
I don't know what area you live in, OP, but if I were you I would ring a local nanny agency, tell them what you're looking for, and ask them if that's the kind of thing that nannies on their books are looking to do (doesn't mean you have to go on and use the agency).
In my area (up north, so might be different in London, for example), there are absolutely loads of girls in the 20 - 25 age group who have a couple of years of nursery nurse experience and are looking at going into nannying. Over the years, I have hired two (and interviewed many more). There has been no problem at all with the fact that I work from home, or that I want part-time hours only (though I've had to be flexible about which days in order to get the nanny I wanted since she already had another part-time job on my preferred days). It's also completely standard that the nanny will do errands/light housework/laundry etc. etc. - making themselves useful and doing the jobs you'd be doing if you were looking after the kids.
My current nanny has been with us 3 years and is fantastic - I hope she will stay for years more. We pay her well, and are very flexible about giving her time off whenever she wants/needs it. The kids love her, she is utterly reliable, and on the days she's been, the house is beautifully tidy (she's a naturally tidy person, I think - unlike me...)
I think that a more traditional nanny - who works full-time/long days, has her own way of doing things (rather than fitting in with ours) and doesn't do any household jobs - wouldn't suit us. I can see why they'd suit someone else briliantly, of course. But what we want seems to be pretty common, and there seem to be plenty of good applicants.