Can't answer if you don't specify which airline you plan to non-rev on. They all have different policies regarding non-rev, pet in cabin, baggage, etc.

Are you an employee of the airline you wish to non-rev on? I don't know about all airlines, but many don't charge their own employees to check bags when non-reving.

And whether you're non-revving on-line or not, you should be able to obtain a copy of the non-revenue travel agreements/requirements for the airline you'll be flying. Check that.

Finding that document ought to answer all your questions.