I've done that run many a times many years ago with various G/F's, one of whom I married !...........second biggest mistake that was !
Mostly done in SE planes, yeah I know 'jabba' that was back when I was young & dumb !:-)
The route as suggested here by the others is the only way to go, Island hop stay within gliding distance of their shores where possible.
Make sure you have 2 ELT's & lots of survival gear. Charts etc as mentioned here also.
Now the important bit. Have an escape plan at all times whilst traveling that route. I've been caught a few times due lousy wx. Once got stuck on YFLI for 3 extra days (VH TIZ,C210) due low cloud/rain. Another time got caught in Corner Inlet (near the Prom)due low cloud at 500ft flying in circles over the water, luckily was able to fly down the coast eastwards towards a strip (can't think of it's name right now) where I was able to land & had to spend the night there.
FLI is a great place to visit if you like privacy & solitude.Lots of history on that Island too,some not so good.
Take clothes to suit ALL climates:-) FLI is the only place where wood rusts!
The Walkers & the Bowmens used to run pretty much the main places there at Whitmark, am sure Stan Walker is long gone. Do a Google search on Walker @ Flinder Island, should yield plenty.
Enjoy the experience but don't go unprepared.
P.s..........don't be tempted to go to YKII, it's nowhere near as appealing !
Wmk2