Under COBRA, you can stay in your current employer's plan for one year after you leave. you'll have to pay the full premium, but beats buying an operation.

Make sure you have continuous coverage. They can't refuse to pay if you do not have a gap in your insurance. I think a gap of 30-60 days is ok.

They can't refuse to cover it as a pre-existing condition, but my understanding (at least pre-ACA/Obamacare) is that different plans can/will have different coverages (so just because your current plan covers treatment doesn't mean your new plan will cover treatment the same way).

I have an opportunity to work for a new company. My primary concern though is that my daughter (less than one years old) has a rare condition that will require surgery in the next couple of months. If I switch jobs, and therefore health insurance providers, could this impact her coverage for this operation?