I think the unpalatable reality is that you are now looking for 'any' school rather than a 'good'/popular school. As mentioned above, most/all 'good'/popular schools will have their places filled for September this year and, in fairness, can't be expected to keep a few places for possible newcomers if they have actual applicants on a waiting list - and things are particularly bad now because of the baby boom in the late 1990s/early 2000s. If fee-paying is not an option, you should probably just apply to every school in areas that you would consider living - then if any of them have spaces (and I expect some will), ask here or on rollercoaster.ie for peoples' views on which is best/least worst. It's not a great selection process but it is probably what needs to be done. The Department of Education has a school-finder at http://www.education.ie/en/find-a-school which will help you find all the schools in each area. Good luck!
Great advice.
I feel for you, you are in a tough situation, its a big move and this must be making it more stressful.
If you end up with your daughter in a school that you are not satisfied with, you can try to get her a place in a different school for 2nd year. A lot of people move house and places do become available. Schools must keep up their enrollment numbers or they risk losing a teacher so they do welcome new pupils. This may sound like a lot of disruption for your daughter, but it may be a better option that sticking with a school for 5/6 years where you know the range of Leaving cert subjects is poor or the science or language department is not good etc.
Also, some people keep places in 2 schools and decide at the last minute and families do move at very short notice sometimes ( these days with the jobs market this is happening more and more)
Schools sometimes have places to offer right up to the day school starts.
Keep in touch with schools that you are interested in and ask about how long the waiting list is.
All is not lost. You will find a school place for your daughter and hopefully ( even if this takes a year), you find a school that you are happy with.