While I don't have prior experience with this topic, selling one's old car and buying a car in Ireland seems like the obvious choice. Yes, vehicles are more expensive in Ireland (though there is a good-sized used market), but the cost of shipping is huge. And once it's there, you have the driver side on the opposite of every other driver, which might make adapting to left-side driving that much harder and perhaps entail other safety issues. There might be other issues with Irish vehicle regulations as well and may need some modification, and Ireland has a very punitive system of taxes and fees for vehicles that are too old, don't meet their fuel efficiency standards, etc.

My advice - sell your car in the US, immediately get to the task of shopping for a new vehicle (and setting up an Irish bank account), and simply rent a car to fill the gap. (This is what I plan on doing.) If you have a credit card with a sufficient limit, you should have no problem with finding a rental.

I would not want to have a left hand drive car in Ireland. So much of driving is muscle memory, and in my opinion adjusting to driving on the left is FAR easier when your position in the car remains the same relative to the road. If that makes sense? You can't always be processing "drive on the other side", it's just not the kind of thing a well-trained driver brain does. I find that putting attention on my position relative to the road is easier. I concentrate on keeping my(right) elbow by the door pointed at the center line of the road,  the same way  I'd do with the left elbow here. 
Also, many US models would feel very oversized on Irish roads. You'll find that the gas mileage of european cars is generally far superior, too, and that adds up when you'r paying over $1.50 a litre.