Okay hi there OP, fellow irish living in Perth! Firstly, you should know that SO MUCH info that has been mentioned on this thread so far is incorrect!! Mainly- you ABSOLUTELY DO get childcare subsidy (CCS) as a PR!! You just aren't entitled to many of the other gov services. But that's fine. Basically as long as you have CCS, you can afford it! You'll also be entitled to Medicare as a PR holder.
The visa you want is either the 189,190 or 186. These are the PR visas. Although the 186 is an employer sponsored one, so not ideal. Generally being sponsored by an employer is absolute hell, but considering you'd actually be PR, it's not toooo bad, because at the end of the day you do actually have the freedom to just quit. Absolutely avoid any other sponsored visa though. You absolutely will not be able to afford childcare unless you have PR.
I think you will be able to afford to live here given the info you've stated. You would probably be able to afford an apartment, maybe even a Unit/Villa. It will depend on the actual salary you get. I think you could get a small rental for $400-450 pw. Yes the market is sooooo tough right now, but if you are only looking for a 2bedroom place, you will be avoiding the most sought after 3/4 bedroom listings. Cost of second hand cars is quite expensive too right now, but you can always find something.
With regards to your child's father- you 100% should engage in a migration agent for all this. It's long and complicated. But it should be fine as long as your ex cooperates. But of course you need to make the decision for you about the what ifs. What if he actually forms a relationship with the child over the next few years. But at the same time you get homesick and want to move back to Ireland. Would you be strong enough mentally to manage through the homesickness if you are forced to stay in Australia? Of course up to you to make the decision, and it might all work out nicely. Australia is a lovely place to raise children :)
With regards to your ex's visa. You need to check with an migration agent to find out if his child entering the country will affect his visa. WHV holders are not allowed to have dependents. At present, his child is overseas, so no issue, but if the child enters the country, there could be. Defo need legal advice on this. Just an fyi, You and your ex won't be able to do any sort of joint visa either if you can't prove ye are together (having joint bank accounts, rental agreements etc. over the course of the last 12 months). Having a child together isn't enough. Just in case you were thinking of trying to add him to your application.
You should join the Irish Families in Perth and Irish in Perth pages on Facebook. Also join Poms in Oz page on Facebook too. There's a million other fb pages too, for all the different visa subclasses. And maybe even one for social care workers in particular. Just use the search bar on Facebook to see! You will get a LOT of ill advice though, like here, people say things as if they are fact and correct, when really the information is wrong or at least outdated. So my advice would be to use these Facebook pages as a guide, but NEVER trust them without doing your own follow on research/consult an agent.
Perth is great to raise a young family, and I think you'd love it here