Yes, you absolutely can bring your pet to Canada, provided it is not something that is prohibited, like an exotic cat or elephant or something of that like
Cat/Dog/Bird/Fish, something of this nature is absolutely no issue. You only need make sure you pet is up to date on his/her vaccinations and get a health certification from your vet in your home country certifying your pet healthy. Most times it is a very simply procedure, occasionally, a pet may need to be quarantined to ensure his/her health but that is rare.