IMHO if you can't deliver it in personally or have a person deliver it for you, sending it with a carrier that has specialised care for live cargo is the only way to go.
With the couriers packages are thrown, crushed, bounced, dropped, disapear and in general mistreated. And then there's the automated sorting machinery that these companies use, which are NOT gentle with the handling of packages.
There is a reason AirCanada costs more, you pay for the fact that it's handled carefully, delivered in a timely manner and insured against loss.
If you're animal isn't worth the extra shipping charges then you should be rethinking getting it.