We have travelled back and forth across the border dozens of times with a dog without being required to show a rabies certificate although we know it could be asked for and we usually have it with us.
Another issue for bringing a dog across the border is dog food
. We have never had a problem bringing dog food into Canada, but there is a restriction about bringing dog food into the United States. When we once made the mistake of bringing an open container of dog food into the US the food was confiscated and our whole vehicle was searched.
Here is the restriction:
The pet food must be sealed in commercial packaging (un-opened) indicating either Canadian or US country of origin.
You might think that you could bring a supply of dog food from the US into Canada then bring it back into the US. This is only true if you don't open the package!
Your dog may get hungry!
Our solution: we don't bring dog food into the US, we buy it in the US.