Your usual bream gear should do the job. You may want to upgrade your leader to 3 or 4kg for fishing around oysters/rocks/warves in the Derwent for bream but otherwise the lighter stuff should be fine. Sounds like a good trip in the making. You'll get to see some awesome little yaking spots on the way down the east coast.
For the trout in the rivers you can use small soft plastics on small hook/light jig heads - say around #4 on 1/24th jig heads. Also a few Celta style lures are good in the fast water. And of course fly fishing - do you fly fish? For trout in the lakes a bigger plastic like a power minnow or squidgy fish works well on a 1/16th jig head.
