Did Australia fight against the Finland in World War 2?

Yes and no. As part of the British Commonwealth, Australia fought against Germany and Italy. Germany and Finland essentially aligned themselves to oppose a common foe-the Soviet Union. During the early stages of WWII, Britain actually gave aid to Finland in defense of attacks by the Soviet Union on Finnish territories. When Finland aligned with Germany, Britain declared war on Finland. Thus, the two become enemies by default. However, they never actually had combat with each other.