Yes Brisbane City Council has similar restrictions in its Public Lands and Council Assets Local Law 2014. The Sunshine Coast and Brisbane local laws are based on a model local law, so any council which has develooed a local law based on the same model law will have the same restrictions. Typically, this would be most councils in Queensland.
In Queensland, Councils can regulate uses which occur on their lands, including those owned by councils such as parks and roads.
It is likely that councils regulate/restrict drone use as if they allow it to occur on one the land they own, it is likely that would take on take on (full or partial) responsibility/liability if something goes wrong. This is the case as they accept the use based on the risks imposed on other potential land users.
Councils traditionally have been very conservative and avoid any risks where possible, as any liabilities associated with these risks are passed directly to the ratepayer.
It is also worth noting that local laws can’t seen to be inconsistent with other laws, however, the restrictions placed on the community can be higher than other State or Commonwealth laws. Tecnically drones can’t be flown in most urban areas as it is near impossible to achieve the flying restrictions inposed by the Commonwealth (Brisbane CC appears to have found some locations where risks are low and that Commonwealth restrictions will be met). It appears that this local law and others just replicate these restrictions.
I also suspect that should one wish to gain an approval from Council, one would need need ro obtain Commonwealth approval first if it is required. If not, then any approval would be conditioned to he consistent with the requirements of the Commonwealth. One would need to demonstrate how the Commonwealth restrictions would be met.