I took a look in the WoodenBoat magazine index for articles about Australian woods and found several by their wood technologist, Richard Jagels. I didn't have issues 46 & 47 but did find issues 95 & 96. A couple of woods that might be candidates for wood stripping are King William Pine and native Red Cedar, if they are not too expensive. People do built kayaks with strips as thin as 1/8 inch, often with a heavier fiberglass layup. It seems possible that you could substitute a slightly heavier native wood and reduce the strip thickness to keep the total weight of the wood about the same. I think I'd stay away from ultra light woods like balsa.

Also quoted by Jagels is Murray Isles, a boatbuilder from Tasmania, who refers to Wood in Australia by Keith Bootle as his "bible for Australian timbers."