No they haven't.
Searching Google for the picture brings up this fallowing blog post which address this picture particularly. It cites the 2011 Australian Crime Report (alternative link) published by the Australian Institute of Criminology.
from the post:
Below is a chart from the annual Australian crime stats report for murders — the short version: murders have fallen 10% just since 2006 and that is raw numbers. Overall murders on annual basis have dropped almost 25% since the late 1990s gun ban.
From page 16 of the 2011 Australian Crimes Statistics Report.
Australia did see an increase in violent crime during the 1990s which leveled off after 2001, with exception to a slight rise from 2005-2007.
This chart is from page 6 of the 2011 Australian Crime Statistics Report.
There is also a page on Snopes addressing a slightly diffrent rumor regarding rise in crime in Australia, a supposed letter from an Australian police officer. From the Snopes page:
In the latter case, it should be noted that the Australia-wide percentage of homicides committed with firearms is now lower than it was before the gun buy-back program, and lower than it has been at any point during the past ten years. (In the former case, the absolute number of firearm homicides in Australia in 1998-99 was the lowest in the past ten years.)
Other claims offered here, such as the statement that "While figures over the previous 25 years showed a steady decrease in armed robbery with firearms, this has changed drastically upward in the past 12 months" and "There has also been a dramatic increase in break-ins and assaults of the elderly" are even more difficult to evaluate, because they don't offer any figures or standards of measurement at all. Do they deal with absolute numbers, or percentages? Do they reflect all incidents of crime, or only those committed with firearms? How much of an increase constitutes a "dramatic" increase? According to the Australian Bureau of Statistics, the proportion of armed robberies involving firearms has actually declined over the last several years:
1995 - 27.8%
1996 - 25.3%
1997 - 24.1%
1998 - 17.6%
1999 - 15.2%
2000 - 14.0%