Also:
what sort of things can you cook?
What attracted you to nannying? If you couldn't be a nanny for some reason, what would you choose to be?
What did you like most about your last job? The one before? Why are you leaving?
What did you like least about your last job? (Can be tricky - either nothing at all if that was genuinely the case or else be honest but very brief in your answer - don't go into any gory details if your last MB was dreadful, for example)
How would cope oif siblings or playdate friends dveeloped an argument?
Do you know other nannies locally?
What sort of activities did you do with your last charges? Are you any good at arts and crafts (but be prepared to back that one up with some sample pictures.)
The thing that I would look for is whether the nanny is able to engage with my DD and whether she does so happily, without prompting. Also important: will I be able to get on with her? The thing that used to bother me most about a couple of nannies I had was they really didn't like it at all if I was in the house - wanted sole charge every minute. Didn't even like when grandparents came to visit from overseas for a few days. I would want someone who made it clear that she was there to look after my DD, in the way I wanted but with a willingness to moot ideas and take initiative when required and also to make my life easier. You might also think about how flexible you want to be about working late - no nanny wants to be taken advantage of but in today's job market it is often very, very important for parents to stay late at short notice - are you happy to cope with that, provided it doesn't happen more than, say, once a week or or 1-2x per fortnight?
Finally, have you checked that whatever salary you are asking is in line with the market where you live?
Good luck, I hope that you find a nice position soon.