There don't seem to be a lot of companies that handle this sort of transport, but I was able to find a few so you can try to get competitive quotes:
Overseas Horse Services, Canada
Air Equine Shipping Services, Inc.
674 Via Dela Valle, Suite101
Solano Beach, CA 92075
888-247-2424; 619-350-2050; Fax 619-350-2055
Air Cargo & Air Charter Services for Horses
Jet Pets, Inc.
9111 Falmouth Ave
Playa del Rey, CA 90293-8617
800-PET-8901; 310-823-8901; Fax 310-305-8297
Serving South America, Europe, Asia, Australia & New Zealand
International Racehorse Transport
8055 West Manchester Ave, Suite 520
Playa del Rey, CA 90293
310-306-0262; Fax 310-306-2003
Happy Horse Equine Services, Inc.
7370 NW 36 Street, #415M
305-597-7115; Fax 305-597-7135
Complete Import and Export Service
3500 Inner Loop Rd
Atlanta, GA 30320
Worldwide Horse Transportation
South Cargo Complex, 4301 ASR Road
Atlanta GA 30326
Providing International Horse Transportation to Europe and Beyond
U. S Equine International Transport Agents
2323 Clintonsville Rd
Paris, KY 40361
859-987-4406; Fax 859-987-4461
World Leaders in International Equine Transport
HFR Int'l Horse Transport
P O Box 236
Brewster, NY 10509
845-279-2492; Fax 845-207-9000
Animals By Air, Inc.
P O Box 60941
Houston, TX 77205
Sprague River Ranch
Sprague, Manitoba ROA 1Z0
204-437-2795; Fax 204-437-2795
15 years Experience in Exporting and Importing Horses from and to Europe
International Horse Transport, Ltd.
P O Box 698
Bolton, Ontario L7E 5T5
800-387-1779; 905-584-2202; Fax 905-584-1373
Serving Canada & the US
Collins Equine Air Trans
P O Box 1158
64-92-928-833; Fax 64-92-928-323
International Air Transport
You'll not only want to find someone you can afford, but you'll want to know they have a good reputation and can handle all of the issues of customs, etc.
Also, you might ship the horse by air from Ireland to the east coast of Canada or the US and then ship by ground from there. This could lower your costs.
I do know of someone who recently shipped a horse from Ireland to the East Coast of the US and I will ask him who he used if I see him.