K.W.
Potty training is a process, and though many will tell you their child potty trained in a matter of days, it did not take them only days to get to that point. They not only need control of their bodies, with both urine and BM, but also need to recognize that "feeling" to be able to tell us they need to go, get their underpants off, wipe, wash, etc.
So if she doesn't care if she is wet in her underwear, it's too early to move her to cloth training pants or underwear IMO. You're only setting both yourselves up for disappointment.
Just have regular potty times every day an give her positive reinforcement for each step that she does. So she is continuing to build those other skills and not have any fear of the potty.
Diapers vs pullups is up to you. Just don't think she'll train in pullups because they really are just diapers. Most moms I know including myself, were not able to potty train without getting rid of them--kids are smart--if they know they can just go in their pants--they will! We used pullups during the day for convenience (much easier to change on kids that can stand) and diapers at night for the absorbency before moving him to underpants.
Try her periodically (every 2-3 months) in underpants (or training pants) and give her a couple of days--if she still doesn't realize or care if she is wet or dirty then, back off and try again. The vinyl covers are nice those first few days at helping save the couch--but just be prepared to clean up some messes....Like you said, you have time. I bet though that by 2 1/2 she'll be more than ready based on what you've said (and that she is a girl)
BTW we tried the underpants at 2 1/2 with my son and had no luck at all, but at 3, he was had 2 accidents the first day and only one the next (still wears the pulls ups for night though). He had never once told me in pullups that he had to go (in fact he would insist he didn't--but once he was in underpants and had a few accidents, he started telling us.