I am doing some research for a novel and need to know since such navigation of this scale is way over my head.

An Aircraft Carrier sails from the RAAF Base Darwin in Australia to Fort Washington near Washington D.C. in America. What is the quickest and best route for such a journey? I am assuming they would have to stop to refuel/resupply at some point as well... especially before the returning journey.

(Yeah, I know it would be fastest by air but that's not what I'm asking).

A rough estimate will do as well! Thanks for your time! :)