Fisherpilot
I wouldn't worry, no employer wants an unhappy pilot. I've left several jobs for better gigs; other than a snide comment, everyone understood. One was a three-pilot deal. The Chef said he'd have one the same thing, 25 years earlier.
But, be honest and upright. Take vacation or some "personal" time for a family matter to go to an interview, do NOT call in sick. Try like the dickens to give them as much notice as possible--two weeks minimum.
Don't be like the guy I "represented" as a new MEC rep. He was at EAL, got an offer from DL. At DL, he admitted that he had gotten his F/E ticket at EAL. DL showed him the door to Virginia Ave. he came back trying to rescind his EAL resignation. Company investigated, saw some suspicious sick time and refused his request. The case didn't go far. Be honest.
GF