I got my daughters done when she was 1 month at Claire's they don't need anything just a signed consent form. They younger the better less pain. My mom did mine 3 days after I was born just make sure you take good care of it.
You shouldn't get any piercings with a piercing gun, they don't get cleaned right and you're piercing their ear with a very blunt object. I'd call your local tattoo shops and see if they'd do it, I know some around me do.