There are two. Just over the hill is Burgmann Anglican School (K-12). It's like any other Anglican school but has a waiting list of about 3-5 years. It's culture and academic standards are higher than government schools but about average for private schools. Next to Franklin in Harrison there is a Catholic Primary School, Mother Teresa Primary, which goes up to year 2 at the moment. It's new (about a year old) so I can't tell you how good/bad it is. See http://www.burgmann.act.edu.au/ and www.motherteresa.act.edu.au (this link seems to have problems) for further information.
There is a new government early learning centre just opened up on Oodgeroo Avenue, Franklin (www.fecs.act.edu.au/) which seems to be well resourced. There is also a government school in Harrison that goes up to year 10 (I think) but everything I've heard about that school has been bad (except that it is new). In the town centre there is a senior college that offers a variety of subjects in a quasi-university setting (www.gungahlincollege.act.edu.au/). Conceptually it's not a bad idea, but having that sort of program means that whilst students are expected to be more self-managing they are also given a few more liberties, so you will seem them in and around the town centre quite a bit. I do know of one family who withdrew their child from a good private school (Radford) and put them in the college simply because the subject's offered were more diverse than was formerly available.