Here is some more information from the Citizen Information site -
http://www.citizensinformation.ie/en/moving_country/moving_to_ireland/coming_to_live_in_ireland/importing_car_into_ireland.html

Much of this is relevant too, even though I wrote it specifically for importing from UK: Importing a car costs

Take into consideration the size of your US car....the roads here are tiny. Unless you are on the motorway, be prepared to ride along some hedges and feel comfortable backing up a lane if you come face to face with another car.

Also the NCT as previously mentioned is very important, and your insurance will be higher since the steering is on the other side.

When shipping your car, you will also be without it for quite some time, especially with a shared container.

We sold our car in the US before moving and took a hit because we did not own it for that long, however we were able to purchase a car in cash the week we arrived that had passed the NCT for under €8000. We purchased an automatic, but if you can drive standard/manual you should be able to find a car for less than that. And on a US license, you are looking at insurance in the 1000-1600 range if you have a statement of no claims, if not it will be about double. We were told by our insurance provider that the cost would be higher if the car had the steering on the other side as well. I am not sure by how much though.

Good point, Kate. I always recommend my US tourist buddies to rent small cars. As small as will accommodate their need while on holiday. My in-laws shipped 2 monsters by all accounts, and had terrible problems on some roads. Roads are a lot better these days, but in the countryside, it'd definitely would be an issue.
Personally I think it's better to do what you did. Just take the hard hit, and be done with it.

There is also the Motor Tax.

As I recall somewhere around 3.0 liter engine and above it starts to shoot up quickly.
It is linked to a word document on this page - http://www.environ.ie/motor-tax-rates-january-2016

Yep, there is a €100 jump between under 1.0L and 1.0-1.1L, then it is ~35-60 per .1 L after that, then a €315 between 3.0 and above.

Our issues bringing our car here were two-fold:

Driver's Licence. You are a new driver here. I focused on the requirements and got my license within 8 months--but know that you have delays even getting appointments for every step. Without an Irish license (for just one family member--they don't even consider licensing status of others in house!) expect to pay full coverage of 4,000 Euro a month for a lefthand drive --only Axa would give us coverage! Driver's license testing process $600+. Parking prices are very high in the cities, gas high everywhere.

Car Issues: Automatics are much more expensive here and hard or impossible to find for many models. Most insurance companies WILL NOT cover lefthand drive cars (see Axa above)--BUT consider learning how to drive a manual with stick on the opposite side, a new car and new driving rules all at once--too much for me so glad I brought our car.

Costs to legally drive the car: Expect to pay $2000 to ship (empty) car, vehicle licensing process $300-500, taxing unless you have a waiver will run you a minimum of $2500 to ???,...adding a few hundred euro into that is advisable. 

For licensing of auto--make sure you have a certificate of the emissions and mileage IN METRIC as NCT will not do the conversion or accept otherwise and car companies here are really separate entities from those in the states legally and product-wise so unless you get a super intelligent, helpful and willing dealership you will be stuck. Also have the original title to the car. Also get a pre-inspection at the dealership as headlight angles, etc are different here--you'll fail, wait again, and repay for every test.

As to size--expect dings, some places literally side view mirrors hit off, BUT so many folks now have SUVs I don't think size is really different unless you have something gigantic. 

Apu, I'm going to guess you mean 4/year not month, right? I paid a lot less than that for 2 US licensed drivers. In the 1200-1500/year region if I recall correctly.

Thanks for all the other great info/tips

On the topic of Automatics - if you drive an automatic for your test, then that'll be what you are licensed to drive. If you want the ability to drive most cars, then as Apu says, consider learning to drive stick.