I was born in India, but moved to Australia at the age of 3 and became an Australian citizen. Is it possible to use my country of citizenship in applying for a green card?

Generally, one is counted against the country of birth (or spouse’s country of birth), not country of citizenship.

There are limited circumstances in which one’s country of citizenship can be used – typically, this occurs when the child is born in a country where neither parent resides. (e.g., Parents are temporarily visiting India, but neither parent was born in, or is a citizen of India.) But, the mere fact that a person left his or her country of birth at a young age would not be sufficient to allow for the use of country of citizenship.