Welcome to the forum! I know very little about ballet training in Ireland, but have some understanding of the education/Leaving Cert process.
It looks like your DD is 14 and in the UK would currently be in Year 9. Year 10 and 11 are the GCSE years, so if you were looking to send her to a UK school, then she would most likely have to start in Sept 2018 (Year 10). There are often a few places available for year 10 - see the thread regarding breaking in to Yr 10/11! Is your DD set on a classical dance, or a broader range?
You could consider schools such as Elmhurst, Tring, Hammond and Royal for year 10, which will offer a good education, dance training and there will be accommodation in a residence hall. However the audition process has already begun, and in some cases, applications may already be closed, so you would have to start now. To be honest, it is very difficult to get into a dance school in year 11.
Alternatively she could complete her Junior Cert, and you could try for post 16 training in Sept 2020. There will be a lot more choice of schools available and this forum has a huge amount of info on the upper school threads. You don't say where in Ireland you are located or how much training/style your DD is currently doing, but I would try and make sure she has access to the best teachers you can find over the next 2 years - most likely Dublin or Cork in the south (I don't about the north). Could you also consider an associate scheme in the UK, where she may be able to come fly/rail over on a weekend to London, Leeds, Birmingham, Manchester to access more specialised ballet training? Although there are more choices post 16, bear in mind there will be an awful lot more competition for places, so good training now is very important.
If she decides to do her Senior Cert as well, then you could look at training post 18 - again a wealth of info on the site about training then.
Friends who are going through the education system in Ireland, highly, highly rate it, and as a dance career can be very difficult, I wouldn't underestimate the value of good qualifications.
Everyone on the forum is really helpful, so ask away if you have more questions. I hope this helps a little.