125 to 600cc
in itself, isn't a problem - it's being thoughtful in choosing a 600 that isn't too lairy, and having enough sense to respect it.
Part of it is what budget you have to spend. The other crucial aspect is insurance - although you've been riding 6 years and have NCB, insurance cost shouldn't be under-estimated.
As you need the bike restricting, your best bet are the twin cylinder bikes - Kawasaki's ER6 or Suzuki's SV650 are ideal candidates for restriction. Four cylinder machines can be restricted as well but tend to be "strangled" in a way that twins aren't. Bandits, Hornets and Fazers are popular first big bikes (four cylinder bikes).
Keep in mind the cost of a drop; although you've done 6 years, a 600 will be significantly heavier than a 125 - faired bikes especially will make your eyes water if it lands on its side.
If you avoid the uber-high-performance 600s, treat the bike with due respect and take your time to get used to it, you'll be fine.