I need to invoice a customer with an Irish address in Euros. Do I charge VAT? If so at what rate? Also does the exchange rate conversion have to be at the date of invoice (as it was quoted at a different rate a few weeks ago?). And lastly should I also include the sterling equivalent amount on the invoice?
gbm is correct regarding the VAT. I would suggest you check the VAT number using http://ec.europa.eu/taxation_customs/vies/
with regards to the exchange rate, if you quoted at a certain exchange rate or perhaps set amount of Euro's then stick to that price as that is what the customer/client has agreed to pay.
Also what are you charging for? Services or Goods?
If you are selling goods that they are collecting from your premises then VAT is charged anyway. Unless you can provide evidence that the goods are being shipped out of the UK, your customer as long as they have a legitimate VAT number does not have to pay VAT - but you will need the proof they goods left the UK to back up the invoice.
Services are charge for as mentioned by the others.
Northern Ireland is part of the UK for VAT purposes, so I presume you are invoicing a company in Southern Ireland.