No you can not, sorry.
This is a postcard swap for adults. I dont think it is fair game to the kid creating, nor the few people that receive kids art but dont appreciate that kind of thing. But please, let your kid make postcards along with you, and send those out to friends and relatives instead. They can be part of your process, and wait together with you to receive your postcards. Encourage them to make postcards with their friends, and swap in preschool/class. Thanks for understanding!
Lets say, if youre 16 or older (and you have your parents approval to join) you can, but I recommend you make the 10 cards before you sign up so you dont forget/run out of time. Let me know if you need any help along the way.