Welcome to Michele's Forum!    

September is a GREAT time to visit Ireland -- Moderate weather, lower crowds and still plenty of daylight.  You are wise to limit yourself to 'only' the Republic.  Although 17 - 18 days certainly would allow to rapidly cover the whole island, I think you will be able to enjoy your visit MUCH more by taking a slower pace.

Dublin hosts a number of 'Ghost Tours' -- some, walking and others, via bus.  The nearby Hellfire Club might be of interest: http://www.hellfireclubdublin.com/

Leap Castle (in Roscrea) is reputed to be the most haunted in Ireland:  http://leapcastle.net/  But, there are plenty of others, as well.  

https://www.irishmirror.ie/news/irish-news/ghosts-most-haunted-places-ireland-6281353

http://www.dailyedge.ie/national-paranormal-day-3989808-May2018/

For car hire, it's important to understand the specific "Terms & Conditions" relevant to Ireland and the various companies -- Particularly those concerning Collision Damage Waiver ('CDW') and the attendant, "Excess".  The cost for a second driver and coverage for tyre, wheel and glass damage is also to be considered.  Note that the typical hire car is one with a Manual Transmissions.  Automatics ARE available -- but, usually at a SUBSTANTIAL premium.

I typically recommend https://www.dandooley.com/  or  http://www.connsirelandcarrental.com/  Although neither are necessarily the cheapest, they both get High marks due to their pricing transparency.  Conn's is an exclusive agent for Hertz and only offers "Full Coverage" rentals -- (CDW AND 'Excess').  An often lower-cost option to Dooley is their Exclusive agent:  https://www.foxrentacar.com/en/locations/ireland/dublin-airport.html -- but they aren't quite as thorough in their pricing information.  Most other companies are also decent choices -- IF you do your 'Homework' -- but you may have to 'hunt' a bit to locate ALL of the final costs and details.