This one surprised me.
I had started writing an answer suggesting that this was most likely a misunderstanding of a claim by Professor Des Cahill to a Victorian state inquiry in 2012:
AT LEAST one in 20 Catholic priests in Melbourne is a child sex abuser, although the real figure is probably one in 15, the state inquiry into the churches' handling of sex abuse was told yesterday.
RMIT professor Des Cahill said his figures, based on analysing conviction rates of priests ordained from Melbourne's Corpus Christi College, closely matched a much larger American analysis of 105,000 priests which found that 4362 were child sex offenders.
Note that this (a) a statistical prediction, based on assumptions, not a simple count, and (b) it was an estimate of abusers, not the number of priests charged with abuse.
This means the first part of The Monthly's claim was false, and the second was at least based on an estimate.
However, as I continued the research to back up these figures, I found that figure on charges may well be similar to the estimate.
Let's start with the easy part: How many priests are there in Australia?
The ABS reported in 1994 that there were 2,005.
Catholic Australia have a web-site that claims there were 3,085 in 2009, and that it has generally been dropping. It includes at least 495 retired priests in that number - maybe more. It references "Official Directory of the Catholic Church in Australia 2009-2010, pp.735".
That is a large difference, and it is difficult to see how to reconcile these figures. It may be a matter of definitions (e.g. whether to include retirees) or one or both being inaccurate.
The figure of "around 3000 Catholic priests in Australia, plus a few hundred retirees" seems to on the high side, given retirees are counted separately, but it isn't a gross exaggeration, especially given the rubberiness of the figures.
"Of these, an astonishing one in 20 has been charged" would suggest at least 150 currently living priests have been charged.
The Catholic Church acknowledges 29 living priests (and an additional 30 dead) as "guilty".
The Catholic Church has released the names of 29 Melbourne priests who it acknowledges are guilty of sexually abusing children. [...]
The church revealed the names of 29 of those priests on Thursday, including repeat offenders Desmond Gannon and Michael Glennon.
[...] However, it says it will not name the remaining 30 priests because several were dead when allegations were made and they did not have a chance to respond.
The church is also withholding the names of priests who were not charged after police investigations.
Twenty-nine is a serious number, but to get to the 150 figure would require over 120 people to have been charged and found not guilty.
If we were to take only the cases the church has admitted to, the answer would appear to be no.
Wikipedia puts the number of priests charged, as of 2011, at "over 100" over all time, but unfortunately uses a broken link to a partisan site as evidence.
As of August 2011, according to Broken Rites, a support and advocacy group for church-related sex abuse victims, there have been over 100 cases in Australia where Catholic priests have been charged for sex offences against minors, as well as others involving non-custodial sentences and inconclusive proceedings.
I was ready to dismiss that evidence, when I found the equivalent reference on Broken Rites Australia's new web-site:
This page gives a few examples (not a complete list) of Broken Rites cases involving Catholic clergy and religious Brothers in Australia. This page is confined to Broken Rites cases - that is, cases in which victims have been supported by Broken Rites. The complete database of Broken Rites cases is NOT available on the internet.
So this list is a subset (selected cases) of a subset (those involving Broken Rites), since 1993 (which means it may include a non-trivial amount of dead abusers.)
They list, by name, 226 (former) priests. Some of the cases (e.g. Br Michael Evans) committed suicide or otherwise died, avoiding charges, but a vast majority of the reports here involve convictions. An additional 5 were acquitted (but should be included in the "charged" count)
To draw a firm conclusion would be pushing the boundaries of "Original Research", especially because all of the figures here are hard to compare (living versus retired versus dead, published versus unpublished, supported by Broken Rites versus independent, etc.)
However, it seems that there is considerable evidence that the number of living priests charged in Australia approaches - if not exceeds - the 1 in 20 figure originally quoted.