I agree with everything Ina says!
KLM is also a very good airline, and also recently had a very good experience with Horizon Shipping (in the Czech Rep.). The biggest thing is to make sure you have all necessary peperwork and vaccines for customs,
A really good person to contact is Johannes Ruf (owner of Erik Nanook Zlata Palz) - he has made the journey to Canada with his dog from Europe more than once.
And next time you fly across the Atlantic, it must be to visit the US!
Have fun!!!!
Marcy