Probably not worth the time or trouble. The annoyance (and I suspect it's deliberate on behalf of the Bosnia-Herzegovina authorities) is that you can't buy insurance cover at the Neum crossing. Instead you have to divert east or a few miles to the Doljani crossing where you can buy cover, and then retrace your route back to the coast road and the Neum crossing. This adds around 30 miles to the Zadar / Dubrovnik route, plus time for queuing / faffing about getting the insurance which is issued off a pad for a fixed price! It's worth taking a look at the UK Government's
Foreign Travel Advice page for more details. As another bit of advice, I'd say your driving time estimates in Croatia are somewhat optimistic. The coast road is spectacular, but can be slow too. There are lots of 70kph limit zones which slow you, and we had to work quite hard to get past slow traffic in places and we were on motorcycles. It took us roughly 6hrs plus stopping time to get from Zadar to Dubrovnik and I'd say that the chances of making the same sort of progress on the main coast road in a car are roughly nil. This means that if you're in Dubrovnik for one night only you'll see nothing of a fascinating city. Personally, I'd try to spend at least two nights there and take in one of the walking tours. It would also give you time to take the cable car up to the war museum on the hill overlooking the town (if you don't know the history of the brutal siege in 1991/92, both the museum and a city walking tour will be a real eye-opener) and a general mooch around.
