Aer Lingus flies direct from Dublin to Orlando, which is about 235 miles away. Aer Lingus does connections, or you could rent a car and see a bit of Florida.
In fact, no one flies direct Dublin to Miami, but British Airways and Air France also offer one-stop options starting at around €600 return, including taxes and charges. Lufthansa, American and United can also get you there.
Aer Lingus, American and United also fly out of Shannon.