Hello, and welcome to the forums. I'm assuming you're new to the forums because I see this is your first post. If by "starting the little one off in" you mean a transport cage to bring him home in, they maybe. I suspect though you meant his first "home". In that case, I would say no, definitely not. You have to think about drainage, heating/lighting, etc. Those are just two issues you'll have to deal with so a critter carrier will be inadequate. Although people have been successful in using small containers like that when raising babies, those keepers usually have a bit of experience. If you don't have the experience, then I'd advise against it. Plus, if the carpets are just 10 days old, I would definitely stay away from even buying one, especially if this is your first chameleon. Most responsible sellers would wait until the babies are at least 3 months old (2 months at a minimum depending on the species). Selling them any younger than that is usually just a way for the seller to make a quick buck. If you've never visited the forums before, you've come to a great place for info. I'd recommend typing a few key words in the search function (carpet, husbandry, housing, etc.) to get a start in researching a carpet chameleon's needs. Hope your research goes well. Most questions you'll have will probably have already been addressed on this forum, but if you can't find an answer to a particular question, the Chameleon Forums is certainly one of the best places to look for answers, and I'm sure you'll find that the people here will be glad to help. Don't be in a hurry either. You'll find good keepers/breeders of carpet chameleons here that have plenty of experience. Occasionally/frequently they'll offer their offspring for sale in the classifieds. I'd recommend buying from them if the animal in question is at least a few months old.
Perry