I have used tussock grass (poa)I cant remember the full name (sorry) its not a traditional lawn looking grass but when it is mass planted it looks amazing
the foliage is glauca if that helps the only problem is that the neighbours get envious cause it still looks good and you dont mow it
I brought them in tubestock and planted them about 10-20 cm apart in a diamond pattern
it took about six months with a few losses but when they grow bigger you can split them up and get more plants
hand pull any weeds around the new bed rather than glypho
and mulch them
if you want a traditional lawn area keep it just make it smaller

For a native grass to grow as a native lawn you have a few options:

Weeping grass (Microlaena Stipoides): Formal looking lawn. 50cm high. Cool season grass

Wallaby Grass (Austrodanthonia Species): Blue/green all year round. Mix with redgrass for good visual appeal.

Red grass (Bothriochloa macra): Warm season grass, turns red in winter also goes dormant

The attached link will sell you seed or contact Greg Boyles native nursery in Epping VIC as he can sell you little plants to place in your lawn.

Here is a link that might be useful: native grass lawns