Is it possible for the relatives (who’s house in which she will be living) to get a dog or a cat, that your cousin can pick out from a shelter? That will give her something to love. Just make sure that the relatives are able to truly care for a pet if they bring one into their home. Although, generally a child who gets a pet should be responsible for its care, in this case, if she shirks her responsibility a little that’s ok. But don’t get a pet unless the pet itself will be well cared for.
Find out what colors she likes and get her a soft comfy blanket and set of sheets and pillowcases, her own set of towels. If you can actually bring some of her actual stuff from home with her (toys, dolls, stuffed animals, art work from her walls, photos books etc.) bring them!
If she doesn’t already have a camera (not just the kind on a phone) get her a decent point and shoot and make sure she has a computer with which to download the photos. Encourage her to take photos of things she’s interested in.
Find out exactly what foods (and brands) she likes to eat. If you get the wrong brand of macaroni and cheese or the wrong peanut butter, it will just add more pain to a horrible situation. Comfort and familiarity are very important at this time. Food offers comfort.
Make sure you stock her room with writing paper, pens and pencils (including some cute colored gel pens and felt tipped pens) some cute cards and envelopes and some stamps. Attempt to get the names and addresses and phone number of her friends and relatives from the state in which she will be leaving.
Let her know that anytime she wants to talk to you, that you will be available (and let her know when is the best time to phone you if you have a job and can’t talk to her then). Let her know that she is welcome to come over to your house and spend the night any time she wants to. Be available to do that, even if you have to break a few dates or give up a few nights out to accomodate her for awhile.
Put up a map of the new city in her room before she arrives. If you are really ambitious, use a bulletin board and put push pins into the places where she will likely be frequenting such as her new school, yours and other relatives homes, the grocery store, post office, doctors office, and fun places like the skating rink, the zoo, the beach at the lake, the movie theater, the church that she will be attending etc.