What a lovely wee girl, Cath. My friends little girl, Allanna, has cerebral palsy, and spina bifida, and she has the fits, but also the most wicked sense of humour, and a bit of a temper if things don't go her way as well! lol! Which I like - that little spark in her! They are quite fortunate in that her dad has his own landscaping business which is flourishing, and there's also a local round table which make donations to local causes, and they've funded different equipment for her, so I know what your neice is missing out on.
Have you thought about applying for Google Ads and Google adsense on her website? They can be a good way of making some money, and to increase traffic to the site, set up a facebook page, and get your facebook friends to join her group, and suggest it to their FB friends, ask them to visit the website, and even if they don't donate, if they click on the ads, it'll make revenue.
Also, make a little video, put it on youtube with an explanation of her difficulties, how people can help, and add a link to her website. Ask in the video that if anyone visits the site, either make a donation, or click on any ads they find interesting (you can't just be seen to be asking people to blindly click on ads, unfortunately). But people will click on ads anyway, if they know it's going to add to the revenue - it doesn't cost them anything.
Anyway, I'll be making a donation as soon as I transfer some dosh to my paypal account.
Good luck, I hope you make your goal soon!