If you were interviewing potential nanny candidates behind your current nanny's back, then that is unprofessional/sneaky/dishonest and I wouldn't want those character traits in a potential boss so right off the bat, I would know we wouldn't be a good fit.
It's like you wanted to have your ducks lined up neatly, then suddenly out of left field you are going to surprise your current nanny with a double whammy. She is not only going to find out she is immediately out of work, but also that a replacement has been hired and is ready to take her place immediately. How mean is that....??! I would be furious. And rightfully so!! Is that how you treat the person who cares for your precious child??
As the new nanny, I would always be watching my back around you. I could never trust you and would always be second guessing you and wondering when I would be on the chopping block next. I would always be suspicious of my job and be checking CL and childcare websites like crazy wondering if you were looking to replace me.
But what about nannies who want to find a better job. They are always advised here to look for a job before they quit. How is that different than a NF interviewing before firing a nanny? Just like a nanny can't afford a break in employment, most families can't weather a break in child care.