First of all, "gun death", "gun suicide", "gun crime" etc are all completely meaningless metric. A murder is a murder, regardless of the tool used to carry it out; ditto for suicide. The only thing that matters is the overall number of crimes, suicides etc.
Now, one thing that you conveniently forgot to mention is that murder rates, violent crime rates etc were all dropping in Australia before the ban, as well. And after a brief post-ban spike (which was likely completely unrelated), they kept dropping at the same rate.
Same thing for suicides. Yes, gun suicides have dropped, but hangings were on the rise (in fact, there was also a spike right after the ban, such that the overall suicide rate was higher - despite the reduction in the number of gun suicides) - and overall suicide rate is basically going down at the same rate as before.
In other words, one thing that Australian statistics shows is that gun ban had zero effect whatsoever on murder rate, violent crime rate, or suicide rate.