Hi Fred,
The closest singletrack to Noosaville is Tewantin/Wooroi in the Tewantin national park. I have not ridden there but from what I have heard its nice and flowy - with a mix of mainly fireroad and singletrack. The closest entrance is 4kms from Noosaville so you could probably ride there. Find a local bike shop and they will probably have a map!
Will you have access to a car or be driving? If so, I recommend the 1/2 hour trip down to Parklands conservation park, just outside Nambour. There is about 30kms of singletrack and just as much fire road to link it all up (the fire roads are shared by bikes, horses and hikers and it gets very busy of a weekend so take care). The singletrack is raw, rocky, rooty and steep (actually - so are the fireroads!) and goes through lots of different types of forest with creek crossings and waterfalls... It is well worth the visit. Beware there is a lot of trail in there and its easy to get lost, though if you go on a weekend someone will be able to help you out.