What is correct?
Australia constantly improves its roads. Australia constantly improve their roads. Australia constantly improves their roads.
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In British usage, a collective such as a company, or a team may be construed with singular or plural: there is a slight difference of meaning, with the focus on the collective or the individuals. This is not normally extended to countries, but I don't see why it shouldn't be.
American authorities insist on a singular.
I don't know what is the situation in Australian English, but I would hazard a guess that it follows British usage.
"Correct" has no meaning unless you specify which authorities you choose to follow.
The correct sentence is: Australia constantly improves its roads.
Australia is singular in this sentence because here, the group of unspecified people that make up Australia are acting as one.
If you were to discuss conflict within, say, a team of Australians, you would want to say "The Australian team are fighting" because although they comprise a single unit, they are acting as individuals.