Most of the Lammys on the road are 125-200CC. However depending on the age you could be looking at a 6v electric system (with points) - which would explain the poor illumination. Many enthusiasts will convert to 12v electrics with electronic timing, which will improve the lighting
I went from Ireland to Holland on a 125 Vespa, (during the summer and in good weather, during the day) - no one can tell you that a 600CC bike isn't too small for touring after that. Really great - but i wouldn't do it again.
Scooters >125cc are ok for the motorway use once you don't have a headwind or a fat passenger (or rider). But one of my main reasons for moving to bigger bikes is safety when heading out on the motorway on a poxy winter night - you've got a lot more power in reserve, better breaks, light height, stability etc.