Did Tasmania Separate from Australia?

No. Tasmania has never separated from Australia politically. It is one of Australia's six states, an island state located 240 km (150 mi) south of the mainland across Bass Strait.

Geologically, Tasmania was connected to the mainland during the last glacial maximum (~20,000 years ago) when sea levels were lower, forming a land bridge. Rising seas (~12,000 years ago) flooded Bass Strait, isolating Tasmania as an island. The Palawa (Tasmanian Aboriginal) people were isolated for ~10,000 years until European contact.

Constitutionally, Tasmania was a British colony (Van Diemen's Land, 1825), then a self-governing colony (1856), and became a founding state of the Commonwealth of Australia at Federation on January 1, 1901. It remains a state within the Australian federation.