Dublin or Drogheda to Belfast International
 

I'd be staying in Belfast for a 11.40 flight rather than having to get up at stupid o'clock for the drive north.

Thanks, after a lot more thought we have booked accommodation in Newry for the night before the flight. The drive time to Belfast International from the hotel is given as 58 minutes even if it takes longer we won't have to get up stupid o'clock.

I wouldn't plan to arrive at the airport at 11 for an 11:40 flight.

You have to visit Newgrange with a guided tour. If you arrive there on the day, unless you arrive very early, you will likely find that all tours for that day are already booked. Even if you manage to nab a tour, it may be five hours later. The only (but expensive) way to be sure to get in is to reserve a private tour, which will be practically an all-day affair that visits several other sites. We visited Newgrange about 10 years ago, but on our most recent visit we were unsuccessful, even though we arrived early.

I'm not planning to arrive at 11am, for the flight, that is the time the baggage drop closes. We can easily leave Newry by 9am.
Thanks for the Newgrange information, all tours are now booked online, and cannot be booked more than 30 days in advance, I have put it on my to do list for 30 days ahead of our planned visit.