What does MHR and GG stand for in the government?

MHR stands for Member of the House of Representatives and GG stands for General Government.

GG also stands for Governor-General, the representative of a monarch in an independent country. In Australia, for example, the Governor-General represents the monarch of Australia.

Currently that monarch is Queen Elizabeth II, Queen of Australia, and is represented in that country by Her Excellency Quentin Bryce, AC, DStJ, the 25th Governor-General of Australia.