I would not ask health related questions. Period. I would call references.

Nannies must expect “absolute honesty” from the parents, as well. If you sense any question about their character, consider that a red flag and run. Always trust your gut.

Employers of a single employee are not subject to the same regulations that employers of numbers of individuals are.

That said, it's never a good idea to leave yourself open to questions of bias or discrimination. So, what you can and should do is write a well crafted job description and interview (candidates and references) very thoroughly based on the requirements of the position. It's perfectly reasonable and legal to use language like:

- the job requires the nanny to be able to lift a squirming child of up to X pounds in order to lift them in/out of bed or highchairs, move them to safety if they've gotten into a dangerous spot, etc...
- the job requires the nanny to be able to nimbly move from the floor to standing, to potentially run after a child, to do multiple flights of stairs during a day, and to be able to physically keep up with the child well enough to keep them from harm and play actively with them
- It is expected that the nanny will take the child on daily walks, in all types of weather (with appropriate garments).
- Of paramount importance is reliability. The nanny is expected to be on time, and to give as much notice as possible if he/she will be absent for illness.

For references:
- How often was Jane late?
- How many sick days did you offer? How did you handle it if Jane needed more sick leave than she had accrued?
- Tell me about the physical requirements of the job when Jane was with you? Did you ever observe her struggling with those demands?
- Can you tell me how active Jane was with your child? Walks? Duration? Down on the floor playing? Able to move quickly if the child got near a hot stove?...
- No nanny is perfect, so what do you wish Jane had brought to the table?
- The things that matter most to me are absolute honesty, complete reliability in terms of punctuality and attendance, a sense of fun and playfulness, and that my child is active and not on devices. How satisfied do you think I will be with Jane on those issues?

I would ask references how many days did the nanny call in sick while she was employed by you ? Was she able to preform all aspects of the job ?

You need to be concerned only if she can do the work, or not. Beyond that, stay out of her personal life.

Spin off from the chronic health condition thread

What are the "rules" of asking your nanny about medical conditions. As an employer of a larger group of people you can't and run the risk of discrimination complaint. Are the rules for nanny employers different? Can you ask about a medical condition? Can you fire or not hire someone who needs accomodations?