Hello. I realise your question has been answered, but I've only just come across this thread. For what it's worth, my DD is 8 and has mild cerebral palsy (spastic diplegia). She was diagnosed just before her 3rd birthday. Although initially I was reeling and could hardly bear to use the words myself, I met someone with an older child with CP who recommended that we use the words "cerebral palsy" with DD straight away. He said it is only a frightening label for adults, not for children, who have no associations with it, iyswim. It felt uncomfortable at first, but that is what we did, and the same when talking to our younger daughter about her big sister.
Of course different approaches work for different families, but for us I think it has been a good approach. It has meant that cerebral palsy is not a scary expression for her, and we haven't had to suddenly spring it on her when she was older; she has always known the words.
As she got older we have talked more about why (probably because she was prem), and how (she understands the nerves going from her brain to her legs don't take as many messages as for people without cp, which means her muscles don't know when to stop being tight, and it is more difficult for her to balance). We also regularly talk about other people with differences (she is very attuned to this), and have made an effort to connect with a couple of other families with similarly affected children.
She is comfortable telling people she has cp - and again for her peers, this is not a loaded term. She even chose to talk to her class about it early this year - made me very proud.
Soon after her 8th birthday she started asking loads more questions, and asked me to buy lots of books about it. I have always tried to be completely open and honest answering her questions - though I feel sad that she is having to deal with some very adult concepts at a young age, and I do think it takes an emotional toll. I couldn't find many books for children, but found a few (all American) on Amazon marketplace. She has found them helpful.
I think she has hit a particular milestone re awareness that this is not something she will grow out of, and she is pretty angry about it. I think she is currently trying to work out where she fits in the world. She is very mildly affected, but she knows she is a little bit different. Currently she asserts that she is not disabled. That is fine by me. I think it is quite a political issue (how one defines oneself, if at all), and it is her prerogative to choose whether or not to use certain labels.
sorry this is such a lengthy response - hard to stop once I start...