Why is Ireland waiting for the EU to approve vaccine and not going with the UK  Approved......[stupid]?

As part of the EU I don't know that Ireland has the freedom to do that before Brussels approves it. 

Because it is the EU commission who are paying for the vaccines, who have ordered doses from two companies and those companies are still testing so it is not as yet ready for roll out....EU countries do as they are told by the EU...so ROI do not have a choice to make a decision about what vaccine they have

Because Ireland is part of the EU, not part of the UK. 

......[stupid]

Brussels bureaucrats are in charge ... this is why Brexit passed, you know

It is because the UK regulatory authority's approval doesn't apply in the Republic and it was probably quicker for them to wait a month for the EU's approval than to examine all the data themselves. The UK has already needed to amend its approval after two nurses suffered an allergic reaction to the vaccine.

The Republic of Ireland is part of the EU and ceased to be part of the United Kingdom about 100 years ago.  Northern Ireland is part of the United Kingdom and vaccinations are under way.