I have a small thyme lawn, in Brisbane. It does quite well here because it's really hot in summer and we have mild winters. Thyme is a Mediterranean herb which like the heat. I suggest in Tasmania, thyme would get leggy and horrible because of the colder climate conditions. Even here, it becomes dormant in winter. You need to avoid the 'normal' thymes, but instead opt for carpet or matting thymes if you want a lawn. But take my word for it - it's not worth the effort. Thyme not only doesn't suppress weeds, but it seems to encourage them (being one of the 'physician plants') and it's almost impossible to keep weeds out of it. Even with my small lawn, it's one of those jobs which needs doing perpetually. And I took great care to prepare the area as thoroughly as possible before I started planting. Also, as thyme ages (like in a year or two after planting) it will die off in the middle and you have to get rid of all the dead matter. The only bits that stay alive are the self-layered bits, which in their turn also begin to die off - it's a continual cycle and you've always got nice bits and dead bits to contend with. I suggest you think twice about it, and in your climate, consider chamomile instead (which gets cooked to a crisp here!) or maybe Corsican mint as a lawn alternative. Definitely try only a very small area first.

Corsican mint would be beautiful. I have it in all the cracks between rocks and pavers in my garden. Does it have to be a 'herb'? Dichondra makes a nice lawn. I have a little miniature native violet, native to South Australia here, Viola sieberiana I think... I've always thought it'd make a good lawn, but probably not overly tollerant to foot traffic.