I have heard a few cases that children start at age two (most of these children have parents who are professional violinists), but it's also a torture for parents to get them to practice and some of them gave up (or parents gave up). If he/she is interested, I think what you expose your child is enough.

I work with very young children (under two years old). I started out playing for them and when they are a little older, I let them hold the bow, told them the rules - only touch the stick and the frog, then I would do the fingering and I would guide them to play songs like twinkle twinkle, the wheels on the bus, may song, etc (mostly on A and E strings for easy bowing). They enjoy that a lot.

However, I am not suggesting that children "should" start at that age. Learning violin requires a lot from a child - concentration, muscle control, coordination of bow hand and fingerings, etc. Most of all they have to practice everyday. Someone said the rule of thumb is 10 minutes per year, i.e., if the child is 2 years old, he/she needs to practice 20 minutes a day, 30 minutes for three year old and so forth; others said at least practice as long as your lesson time (most lessons for young children are 30-minute long). Young children have short attention span, so you can't expect them to practice it all in one-thirty minute practice. If you break it down to 5 minute for each practice section, for a 30 minutes practice you will be practicing with your preschooler 6 times a day. If you just let your child take lessons and not practicing, that it is not only a waste of money but also a waste of time. I have seen children insisted to have lessons but would not practice and after two years of weekly lessons they have just finished learning twinkle twinkle.

I would say what you did with your child is great and expose her/him with a lot of good music, reconsider it when she/he is four or older. Remember, if you keep doing it, your child will stay interested.

It's just MHO.

I want to add a few more cents:

1. provide your child a violin appropriate for his/her size.

2. it does not harm to show him/her the right way to hold the violin and bow. Good habit starts from the beginning.

When I let the children hold my violin, I always make sure their hands are clean (I got mold on my bow once because one of the kids had snorty hand:)) explain to them why I don't want them to touch the bow hair, or the body of the violin. I want them to respect violin and the proper ways to handle one when they see one or have an opportunity to handle one. To me, there's a difference between a toy and a musical instrument, and children could learn at very young age how to respect a violin.