Boffin, I had a nanny for Ds who brought her own child. I didn't recruit her 'cold' as it were -- she'd previously worked at the nursery my older dd attended, and then left to have her own child. She'd done some after-school care for dd1, and then started working for me on a more full-time basis when ds was born.
In terms of the logistics (child sickness etc) it's not much different from having a childminder. As long as you talk all the possibilities through beforehand then it's fine. Do bear in mind that if you have the nanny working in your house, then you have to shoulder the additional costs in terms of lighting, heating, toys, art materials etc etc which you would get as part of the package with a childminder. But obviuosly you also get childcare that is geared to your needs rather than several families'. Horses for courses.
Yes, it was cheaper than having a nanny with no child, but not half as much iyswim. I paid her what she asked for -- can't remember now how much, but it was maybe 2/3 of the going rate for a sole charge nanny? Might have been in the region of £5 per hour instead of £8, but it was a good few years ago anyway, so rates would have changed. I've tended to err on the side of generous with childcarers anyway, I like them to be happy.
Other things to watch out for are: it's easier imo if the nanny's child is not too close to your own in age more like a normal family setup, and less obvious competition. Talk through potential clashes naptimes of one dc vs toddler group of another. But again that's not too different from a childminder situation.
You also need to sort out who's paying for the food etc consumed by the nanny's dc, and who's providing and storing any extra equipment (double buggy, toys for a different age group etc.) You want someone who's pretty scrupulous in terms of tidiness and organisation as well otherwise it has the potential to be deeply irritating.
It was a great arrangement for us, all things told, until it came to a natural end a few years on -- nanny moved away and her dc started school.