You can do it on your GSXR. "Any bike will do" (C) G. & S. Johnson. :-) You can pick a route that's tar seal just about all the way.
I suggest you read the discussions in this forum and some of the stories of people who've already done this trip. Then think about what areas yo want to visit and things will become clearer.
For us it came down to: where on this trip do we want to go? We decided to want to go to Ladakh and do some of the dirt roads in SE Asia, so we decided on trailies. It's not my first choice, as I found out I don't like the big singles (they refuse to run slowly), but a Transalp is too big and heavy for my other half.
A trailie or a smaller bike gives you more options on where you can go, but a bigger bike may be more comfortable. You want to be able to ride very slowly and handle very bumpy surfaces.
Salut from Southern France, the bikers' paradise,