You would probably get more and better responses on rollercoaster.ie which is specifically about all aspects of parenting. It's been a while since we employed someone to mind our kids at home but I expect you would be looking at at least €350 to €400 per week - maybe more - plus, as pointed out, employers' PRSI - and the hassle of doing the payroll for your employee.
An au pair wouldn't be suitable for fulltime care of a newborn - they are limited to 30 hours per week.