Here's the site of the growers we use :
EucalyptusThe site gives a lot of useful information on eucalyptus.
There is a short section on transplanting (see the FAQ). Be not afraid! They say that transplanting is difficult after two seasons.They mean two seasons from when you'd buy a plant from them, not two years from seed so you may well be successful without trouble. (They don't send saplings out until the trees are about 2 feet tall).It's best to wait until March (in Britain, anyway: but see the site

)
Your eucalyptus is likely to be
eucalyptus gunnii which is the species that is found almost invariably in garden centres and plant nurseries, being easy to grow and quite hardy.It is quite a fast grower: reckon three feet or more a year for a young plant that is settled.Most eucalyptus are fast growers. (The
dalrympeana at Newmarket made 40 plus feet in nine seasons from purchase from this nursery

. This species is a particularly fast grower, even in Britain)
Good luck with it! If it's happy a eucalyptus makes a fine tree or shrub with attractive bark and pleasantly smelling foliage. It's sort of evergreen in that it doesn't lose all its leaves but those that remain tend to go reddish and may look a bit scruffy sometimes.