I am the assistant coordinator for my local Project Linus, and we just recently tackled some of these weighted blankets. I learned a lot in the process.
First off, one member made one from the pattern with the sheets inside, and it is very nice -- it's heavy and it's all washable. It's also kind of costly (you have to buy a lot of sheets) and it's pretty darn heavy.
Another member made one with the pellets (also an expense) in the beanbag style described above by misskira. That worked out well, too.
We also made some with supplies we got at a local feed store -- dried peas, which made a nice round ball, and rolled wheat, I think it was. Both were about $4-6 for 10 lbs., comparable to rice if you can find a deal on it.
Some people suggested not using organic material because they can mold, but the organization we were making them for had one with rice that they'd been using for years, and they were fine with organic material. They also told us a few things about shape and size.
I ended up making two styles -- one, kind of a small pillow shape, about 10" by 14". It was just a lump, but the kids like to curl up around it. I made another that was a long snake-like tube (with the bean bag approach), and the kids wrap it around themselves. While we were there, we saw two small kids hold them and cuddle them, which was both heart-warming and satisfying to see that they worked as intended.
My point here is don't stress about it. Anything you do will be helpful, and you can learn as you go. If you make something she likes, you can keep improving on it, or if it doesn't work, you can try something else.
I will also say, if you sit with a heavy blanket on your lap, you will quickly see how calming and relaxing they can be.
Good luck!