Is this plant a native?

B.M, Buninyong. 

Your tender, fleshy plant with tiny white five-petalled flowers growing from the top of the unusual round leaf is called miner’s lettuce.

It is a member of the Portulaca family, a weed from North America. Its botanical name is Claytonia perfoliata.

Miner’s lettuce appears each spring, and is flourishing this year because of wet conditions. As its name might suggest, it is edible. It earned its lettuce name at the time of the Californian gold rush, when it was eaten for its valuable vitamin C.

It is still cultivated and eaten in some places today. It will turn reddish, and wither and die, when the ground dries out, later in spring.