I would say that 3 years full time flying shorthaul is about the stage at which a transfer to a solely LH fleet could be done - wouldn't recommend it with much less than that.
LH flying is 'operating the aircraft' and a way of life more than 'hands on flying' which is why you need the experience of lots of sectors to fall back on. It takes a while to get used to - and no - it doesn't suit everybody. I would however recommend that you take the opportunity to find out for yourself, and not to listen to other peoples perceptions, as they may well not match your own.
You will never feel quite as skilled as a proficient SH pilot, operating as an FO you may only handle 1 or 2 takeoffs and landings a month as compared to 20 or more in SH.
By flying LH you do add quite a few new dimensions to your portfolio though, some of which spring to mind as being Africa (the ITCZ, elevations and HF comms
), Russia and China (language and metrics), North America (volume of traffic, rapid fire ATC and rwy changes, uncontrolled VFR traffic within 500ft etc), Australia (ATC think they fly the aircraft, Aussie rules!).
Throw all of that into the mix and then fly a Carnarsie approach to limits with a stonking tailwind into JFK and you still get enough excitement.