The sentence that is written correctly is C. My father has just won a trip to Australia.
A. is wrong because Australia is a proper noun and should be capitalized.
B. is wrong because father in this case is not a proper noun and should not have been capitalized and Australia is a proper noun and should be capitalized.
D. is wrong because father in this case is not a proper noun and should not have been capitalized.
Hope this helps.:)