Hmm, I don't immediately recall an instance of Cera saying she's the oldest (I'm assuming this is concerning the five main characters here), but let's see if I can find some justification:
Spike: obviously younger than any of the other four.
Littlefoot: roughly the same size as Cera (in the sequels at least, in the original she seems to be noticeably smaller from my recollection), and from a species that is supposed to grow to be way bigger than threehorns.
I can't think of any justification for her to think she's older than Ducky or Petrie. Sure, she's bigger than them, but they're both from smaller species in the first place.