From Zagreb to Dubrovnik in 6 days

I am looking for some advise. My girlfriend and I are taking our trip and we have 6 nights in Croatia.

My idea is to fly into Zagreb and rent a car, making our way to Dubrovnik via Croatian coast.

Is this enough time to see a decent amount of the coast whilst allowing one night in Zagreb and one night in Dubrovnik or is it too much of a rush given the amount of time we have?

Thank you for any ideas