You should check out face to gif. Doesn’t need much for explanation, so just go check it out. But, in short, it records GIF animations from your webcam. You can see one in action here!
The GIF’s are fairly large, I used this tool to optimize them a bit. This took the files from 3.0MB to 946kB.
My daughter will absolutely love this. Afraid she’s gonna make some huge stuff though and break face to gif.