WOW - I was about to say that I would never purchase a children's machine until I saw that your daughter was 3yo. I might be interested in one of the chain stitch machines for a child that young.
I like the Brother CSI 6000 - inexpensive and light weight as well as a decent little machine but I have never worked with a child that young. My DD was about 7 when she really started on my Viking 6370 and is still sewing now 25 years later (on that machine-lol).
What a great thing to share with your young daughter - good luck!!