From a strict public health standpoint, if such a tax is NOT indeed solely a punitive measure to force compliance, then there should be absolutely no exceptions. Your kids are not eligible for the vaccine? Too bad, maybe you shouldn't have had kids then? Why should the vaccinated people have to support your unvaccinated kids?
Of course that won't happen, because this is NOT about public health, it is politically driven, and there is a convenient created "other" class to blame and target to give the illusion of doing something to fight covid.