I would suggest you also submit your question to the EU's free legal advise service
http://ec.europa.eu/citizensrights/
You will be travelling with your EU citizen daughter, so your application for a visa can be very simple (though it may be time consuming if you want them to follow the law). Your daughter has the right of free movement in the EU, as do you when you travel with her.
The following information is based on a successful visa application made to the Irish embassy in London. The minor child was a UK citizen and the parent was a Colombian citizen. Because your Irish daughter has been exercising her rights to live in Austria, the same conditions hold true in your case.
Everyone travelling requires a passport. You must also submit your daughter's birth certificate to prove your relationship with her. Photos. Application form (A number of questions can be left blank though the embassy will not like it).
They will likely ask for bank statements, and a letter from your employer. They will also ask for confirmed reservations in Ireland for specific dates or the name of an Irish reference, as well as flight tickets. You do not have to provide any of this information if you do not want to.
The visa was issued in London without providing any of this information. You can tell the embassy very clearly that none of this is required for the issue of the visa under EU law [specifically
Directive 2004/38/EC as transposed into Irish legislation
S.I. No. 656 of 2006 — European Communities (Free Movement of Persons) (No. 2) Regulations 2006]
If you don't provide the extra information they "require", you will likely have to push them and complain to Solvit, but in the end they will still issue the visa.
Each of the visas issued should be done at no cost. If they ask for any money you should refuse and immediately contact Solvit.
The service you get from the Irish embassy may be very good, or they may be both very rude and quite ignorant of Irish law. In the end they
must issue the visa to you, for free and without you providing any other information than proof of your relationship to the child.