For a serious injury like that, you should try and find a veterinarian qualified to deal with reptiles. You may want to check local animal rescue services for recommendations.
Here is some specific advice about injuries to chameleons, including cat bites:
I have seen chameleons (and other reptiles) with very serious burns, cat bites, cuts, and other injuries and people do not seem to consider them emergencies. ALL injuries of this kind (especially cat bites) are capable of getting infected, becoming necrotic, and causing death. Additionally, they are also very painful, even if reptiles don't show pain like other animals. All of these injuries should be brought to the attention of a vet, so antibiotics, ointments, or surgery can be prescribed if appropriate.
I have seen so many really serious and horrific injuries and infections in reptiles, whose owners think that these injuries can be treated at home with something like peroxide and neosporin. They need proper antibiotics or other more serious medical intervention to save them, and most people simply do not have the products or experience to treat anything like this at home. Using the wrong product could be even worse than doing nothing. Again, go to a vet.
Regarding calming the chameleon... this is a wild animal, not a domesticated pet. Furthermore, it is injured (possibly quite severely). The only way to calm it is to leave it alone as much as possible. It will perceive you, your daughter, and especially your cat as a dangerous predator, and even seeing you will likely cause it considerable stress in its current condition. I suggest putting it in a box (one that lets air in, of course, but which it can't escape from), and bring it to a vet ASAP.