Ditto on the dog food, especially going into the US. We took a small baggie of dry dog food with us once and got caught. We were detained for over an hour and thought we were going to be sent to Guantanamo Bay. Not fun.... Apparently some people were dumping out the contents and putting in banned substances so they stopped it altogether.
Some types of dog food are banned. There is a limit on the amount too. Lamb into the US is a nono. There are rules on the country of origin.
Otherwise, you just need to have up to date vaccination records. We take our dog back and forth across the border lots and have never once been asked about shots.
Info. here:
US border dog rulesCanada border vaccination rulesCanada border pet food rulesFWIW, fruits and vegetables are a problem and it's best not to take anything across the border unless you have studied the US and Canadian allowable lists in detail. If you haven't it's a good idea to visit both the US and Canada gov't sites for what is and isn't allowed to enter for everything.