In the base game if you conquer Australia early, you gain the advantage of 2 extra units a turn with only one territory required to defend it.
Does this change at any point in playing the Legacy game?
Yes, depending on how your group places their stickers.
Initially, the game makes the Australia problem worse, not better. This happens because a player wins when they have 4 Victory Points instead of when they remove all opposition. It is relatively easy to sit back and consolidate your forces in Australia, then attack to get 2-3 Victory Points in a single turn and win before your opponents can counter-attack.
As the game progresses, there are increasing opportunities to "ruin" Australia. Many of these actions can only be taken by the game winner, and many can only be taken once. If you want to de-power Australia in your game, you either need to win a significant number of games or persuade others in your group to help you.
Starting from the very first game, you can place Ammo Shortage scars in Southeast Asia and Indonesia to make Australia less defensible. More scars become available as the game progresses. Game winners also have the opportunity to remove positive scars from Australia.
Scars and other stickers also restrict starting positions. If you fill all of Australia with stickers, no player may start there.
In your first game, all territory cards are valued at 1 coin. However, the value of cards will increase with each game you play. Put high coin values on territories distant from Australia to disincentive this strategy.
There are more (and more significant) ways to ruin Australia, but these are discovered during play.
Continent bonus modifiers: One of the options for a winning player is to modify a continent bonus by placing either a +1 or -1 sticker on it. Placing the -1 sticker on Australia and reducing its continent bonus to 1 is a huge disincentive.
Drafting: After several games, you start to "draft" for placement order, play order, side, and starting troops and coins. A player who picks "first placement" to get Australia is giving other advantageous options, such as "first to play" or "most starting troops". This is particularly dangerous at the beginning of the game. A player with a large army and earlier play order can potentially wipe you out before your first turn!
Sea Routes: You have two opportunities during the game to add sea routes. One is granted to the player who completes the "Explore the World" mission, and another to the player who opens the "Alien Landing" packet. These can be used to create "back doors" into Australia, making it more difficult to defend.
Nuke: The first time 3 missiles are used in a single battle, the contested territory becomes fallout. Fallout is very difficult to inhabit and almost single-handedly counteracts to continent bonus of Australia.
Without spoiling too much, yes. Some of the things that become available in the Legacy campaign help disrupt any strategy that becomes too dominant, although sometimes it may take co-operation on the part of the players who aren't playing that particular strategy.