I would do as @JacinLarkwell suggests and get someone to watch them for you. Someone who you trust, and give them a rundown of what they need to do before you go.
How long is your trip?
I'd leave chicks (not sure what baby quail are called) in an incubator for 12 hours tops. I've hatched...
A quick google search (I don't have quail so I'm not sure how accurate this is) says 18 days is the incubation period.
I would not be hatching eggs just to travel out of town when they hatch. Sounds like a recipe for disaster.