This is overblown and it hasn't even started. It won't (well, very, very unlikely to) bring down the government.

There you go, that's the long story short.

But, it'll be a PITA for the government and may induce some Australian market volatility (as if ...)

The dets (bolding is mine) ...

  • Opposition is considering a High Court challenge against a Coalition MP's right to stay in Federal Parliament, in a move that would put the Turnbull government's slim majority in peril.
  • If Dr Gillespie was disqualified it would spark a byelection in his seat ... potentially bringing down the government.
  • the Nationals would be well-placed to retain the seat

More here: Turnbull government at threat as Labor plans High Court challenge