As @user1291332 has stated Ireland is a safe place to travel just try to avoid the city buses at night if you are on your own. While there are few incidents on them a taxi would be a safer option though a bit more expensive.
Kerry isn't as well connected as the major cities (as you would expect) so it might do no harm doing a bit of research about where you want to go and when. At night your best bet again are taxis as there will be little to no public transport services available.
Also be careful at night to whom you are talking to, avoid suspiciously looking strangers.
Just treat your safety as you would if you were at home and you will be fine.
Here are some other useful links:
National Rail Network (Iarnród Éireann)
National Bus Network (Bus Éireann)