Welcome to my forum. It is possible to fly to Dublin from London and spend a few days there. You will definitely not see "Ireland" in just a couple of days in Dublin. There is an old saying "Dublin is not Ireland and Ireland is not Dublin". You will get a city experience, unless you get into the countryside.

You can check on flights at the Dublin Airport website: http://www.dublinairport.com/home.aspx  As always, prices of flights depend on many factors such as time of year, time of day, airline, etc. Check on Aer Lingus and Ryanair. Beware of Ryanair's luggage allowances and read all the fine print.