Sadly the answer is no. There are limited places at the Winter Olympics and places are allocated on a nation basis. This means that a group of athletes from a country needs to be in the top 22 nations by earning points in the IBU or World Cup competitions in order to secure a berth at the Olympics. Australia and other nations such as the UK aren't in the top 22 and so on this occasion Australia misses out.
Occasionally there may be wildcards or a nation gives up it spot thus giving countries like Australia an entry. The Australia Biathlon Association is working hard to build a new generation of young athletes who will provide quantity and quality and earn those Olympic spots.
Of the current crop the best biathletes are Jillian Colebourn, Darcie Morton and Damon Morton. They are all quite young, in their teens and twenties, and so there is time to work towards the next Olympics and the one after that.