Claire is a small, light brown fox with cream-tipped ears and tail and shoulder-length brown hair. Her usual outfit consists of a purple blouse with a white ascot. She almost always wears her glasses. Without them, her eyes appear small and beady as first seen in "Someone's Stealing My Stuff" and second seen in "Buds Before Studs".
Claire appears to be shy and soft-spoken. She has a submissive attitude, doing whatever her mother tells her without question. She has a notable crush on Foo.
In "Princess is Better Than You", Claire says that whenever she fails at something, she has to write a report on how she can improve next time, which is a rule set by Claire's mother. She also apparently has to write a "victory report" whenever she succeeds at something.
It is also revealed in "Princess is Better Than You" that Claire's mom does not allow her to watch television because of it rotting her brain.
Her age is 10, as proved in the flashback in Technoscare where we see some of the kids as babies, Claire says "we're only three" suggesting at that point she is the same age as everyone else onscreen, which includes Harvey who is 10 at the present date.
CH Greenblatt, the show's creator, has confirmed himself that Claire has two moms. One of the times he mentioned this, he said that "One is very nurturing and one has very high expectations. Granted this is all stuff I thought about and never got a chance to explore. I wanted to finally meet her mom and have everyone surprised that she’s so sweet. Then we realize there’s a second mom who is the taskmaster." The source for that statement is here.