I have looked into this before and you are not going to like the answer.
It is illegal to ship homebrew interstate depending on the states involved. That is what some State law says, but you will find people who do it all the time.
It is illegal to ship any alcohol via USPS.
It is against the policy of Fedex and UPS to ship homebrew. That being said they do it all the time. Apparently contents are described by the customer as "live yeast samples" - what they don't know does not hurt them

To ship from Canada to The USA could possibly be considered smuggling unless you go out of you way to insure all taxes and duties are paid. Most likely if discovered the contents would simply be seized, but there is to potential to get in serious trouble so I would not risk it.
The "Beer of the Month" type operators are shipping commercially produced product and have special arrangements with their shipping companies, the correct permits and are paying all the duties and taxes - it is a completely different situation.
Mostly the issue with shipping homebrew is the Sate/Feds want their share. I can't imagine that sending a few bottles of beer is going to get you in legal trouble - but it can't be ruled out. Yet if it were not for people doing this Homebrew competitions would only be local events, and clearly that is not true.