We pay our nanny, who is a younger cousin of my husband, $11/hour. She's 21 years old and has no college education, but she's very bright & is really great with our 3 year old. Plus we feel really safe knowing we have a family member here when we can't be... I think we're getting a bargain, but truthfully it's all we can afford to pay her. We started at $10/hour but after the first year we gave her a raise. We also give a week's pay for Xmas and a smaller cash bonus for her birthday.
I've heard of a friend paying only $8/hr for a full time nanny, but that was in glenview. Most everyone else I know pays more than we do and also gives weekly spending money and a generous holiday bonus.
I agree with you that someone with your education and experience should be paid a lot more than $7/hour (I'm a college professor myself). But I also know that many people simply cannot afford the high cost of childcare. If someone only earns $12/hour at work and has to pay that to a nanny just to have healthcare coverage for their family, things are really difficult. I've been in that situation and it's not an easy choice to make. Daycare isn't affordable either, at least not quality daycare...
I'd say that you should try to find a family who is able to pay what you're worth (at least $10-15/hour) and that will really value your education and experience. I know we feel like our money is very well spent (and we would be miserable if we had to send our son to daycare every day....). For $7/hour, it probably isn't worth you having to find care for your own children : ) Good luck!