You need to apply straight away, I think now is around the time they start recruiting for the summer. MancMoose is right, once your in you find out about more job vacancies internally.
I know theyve been advertising for ground handling agents, seasonal dispatchers and central load planners recently. Heres the link...
Swissport International Ltd. - Careers - Jobs<br>Search and Apply
Any questions just ask, if you do opt for ground handling, I'd recommend going out on the ramp, but thats just my personal opinion!