Yes.
The closest airport is Kerry Airport, which is approximately 1.5 hr drive from the Island.
If you're planning to take some time before or after the wedding to tour the country (and we really recommend it!) the drive from other airports is not very long. Dublin Aiport: The most direct route takes 4.5 hours Shannon Airport: 3 hours Cork Airport: 2.5 hours
Train rides from Dublin to Killarney take about 3 hours. You could then get a taxi from Killarney to Valentia Island for about €100. This drive is about 1 hour. http://journeyplanner.irishrail.ie/webapp/ Buses are also available, times and prices vary https://www.buseireann.ie/
If you plan to explore for more than just the days of the wedding, renting a car makes the most sense! Be aware that the roads are narrow and you will be driving on the LEFT (also most rental cars are manual transmission unless specifically stated).
Hope for the best, but expect some rain! Ireland can be unpredictable, but you can certainly count on at least some rain. It is best to prepare for a range of weather and pack layers to handle temps between 45-75 degrees Fahrenheit.