If you can't do some sort of on-site review of the photos, then definitely do packages. I would do "pre-paid" packages where folks get a discount for paying in advance. That way, you can tap into the impulse buy to raise more money for the shelter.
If you plan to do on-site reviews, you will definitely need an assistant that is competent with the computer and software you'll be using for the reviews. Since this is a rescue fundraiser, you might even be able to get someone to volunteer to help with this part.
Whatever you do, back everything up before you start doing anything with it on the computer.
Since you said this is your first time I've got a list of questions you might want to think about:
Do you have any idea how many people / pets to expect at the event?
How long does it run?
Do you have / need access to power? Backup batteries for the laptop, camera, flash?
Are you shooting indoors or outside?
How much space do you have?
Will you be in an area that you can close off to pets that are not in the photo at the moment?
Is "Santa" good at handling the pets?
Will you have a backdrop behind Santa or just whatever is there?
Do you have treats, squeaky toys, bird calls or whatever to get the pets attention?
I'm sure there is a ton more, but that's off the top of my head.