Congratulations! Sounds like things are going swimmingly. My daughter potty-trained easily at 2 years/3 months. We're lucky. I would not put her diapers or pull-ups when you go out. I think it's confusing to get the message that using the potty herself is, essentially, just for home. And let's face it, she's going to need to use public toilets sooner or later. I really believe you'd better off showing her how to do that in as sanitary a way as possible (putting paper down on the seat, for instance, NOT squatting. If I take my daughter to one more pee-spotted public toilet seat because someone squatted, missed and failed to clean up after herself, I'll scream). Handwashing, hand sanitizer, the usual. My daughter is really good now in public restrooms. She knows the drill. She wears a pull-up to sleep - after my pediatrician told me that the evenings will take care of themselves naturally, as her bladder develops and can handle 8-10 hour stretches. So, no drinks two hours before bed (though there are times, of course, when you make exceptions. But, as a rule, try to limit drinks before bedtime).
Anyway, best of luck to you!
J.