For this time, Sam shows vampire fangs in her mouth when she gets up to smile for the beauty pageant.
The prince's name is Aragon. This may be a reference to the Inheritance Cycle, a popular book series by Christopher Paolini, where Eragon is a dragon-riding swordsman. This link is later enforced when Dora transforms into a blue, Saphira-like dragon with Sam riding astride her back.
When in human form, Princess Dorathea goes by the name Dora Mattingly. This is a wordplay on the slang term 'doormat', which is somebody who is overly submissive to others' wishes. This goes along with Sam's rant about why she hates beauty pageants: "Other than the fact that they turn girls into shallow doormats and boys into drooling idiots?"