Hi lulupointu,
North Queensland is a big place, you might have to be a bit more specific. What sort of machine do you have as this will possibly determine your options too?
Are you after gold or coins/treasure? If the latter you can try any beach or park near you, just don't leave a mess and council workers will probably leave you alone.
If gold is your target then in general terms the only state owned (government) land you can automatically access once you have a Fossicking Licence (you need one of these to hunt for gold in Queensland whether you go looking on private land or government land) are the General Permission Areas (GPA) at Clermont which is really central Qld.
All other state owned land requires more specialised permissions and more fees and charges. Most Qlders have to find private land on which to get permission and detect upon. There are big cattle properties that allow people to detect upon them for a daily fee. There are some of these around Townsville, Forsayth, Georgetown and other places. Search this forum and you will find references to these places if they are near to you.
Good Luck,
Troutman