Please check your assertions more carefully:
After the passage of the Omnibus Consolidated Appropriations Act of 1997, which included the Lautenberg Amendment, a conviction for misdemeanor domestic violence is a lifetime prohibition on firearm purchases and possession. Domestic violence is the only offense for which a misdemeanor conviction is a prohibition.
Use of Australia as an example of suicide reduction through gun legislation runs into a problem: the state of California. California has passed numerous gun control laws and the use of firearms in suicides has declined (Yay!). However the overall suicide rate has risen faster than the national average (Boo!). Part of the increase is due to the rising rate of suicide among women, who are less likely to use a firearm than men. Poison (drug overdose, alcohol and drugs, etc.) is the method of choice for the most women. The rate of suicide by suffocation (usually by hanging) has jumped 57%.