Plus there are many countryside areas with no oil.
Whether or not that translates into more risk for your exposure to small particles is probably related to where you are (e.g. are you inside the house while the wood is burning, probably, so you are close to the source of it and probably have a lot of small particles around your house that get brought in every-time you open the door).
If its so rural that its just you for some distance then this might offset the fact that your wood burning stove is (probably) not providing any sort of filtering that a catalytic converter, control systems to more fully burn the fuel (so there aren't as many byproducts), or other devices normally used to remove byproducts of combustion. So it comes down to which of those byproducts are most toxic to you comparatively to other forms of pollution, the density of those particles and where you are in relation to them is going to determine your daily exposure in your environment.
I don't know of anyone who uses a wood stove. Most would use natural gas, propane, or electric. Electric is common until you get too far North, then it's cheaper to get fuel.
It's very nice to live out here. You can see the stars and breathe fresh air.
Source: live in rural town.
Admittedly with the current climate collapse gaining pace at breakneck speed, it's possible that this may be the 'new normal' for the Australian bush very soon.