A new gixxer 750 is a nasty bike. Sure you can ride it, but will you ever bring it over 11000 rpm in a tight 2nd gear right hander? Probably not. You've ridden the 250, but how many miles? Some people ride the 250 for two years and think they can jump onto a liter. HA! The only thing is they put 2000 miles on it in that two years. I would suggest at least 10000 miles before upgrading. If you got that than great. The thing with the 600 is once you get use to it you will be able to thrash it, ring around corners, and man handle it. That is alot more fun to me, than putting through that corner at 5000 rpm. Valentino Rossi didn't start out on the 500 bike first. He started with the 125 to the 250 then the big dog.
I've had three bikes so far: 85 Interceptor, 01 f4i, and now a 05 636. When I get to 40000 miles on the 636(assuming I don't write it off), hopefully next year, I'm getting the gixxer 750. Then after many, many miles of the 750 I'm going to get a liter bike. You'll be a better rider if you start out smaller. You'll be smiling when your going around the outside of a liter on your little 600. He might catch you on the straight, but you get to go around the outside again.