I think that this is an important step in learning Chinese.
This is beyond "Teach your child to read Chinese". When they grow up, they should also be able to express themselves using Chinese.
However, writing Chinese characters are difficult for kids and may make them frustrated.
Instead of learning writing the Chinese characters, kids can learn how to type them first.
A good method is hanyu pinyin. Even you are learning the classic not simplified Chinese, you can use Hanyu pinyin to input Chinese.
I taught my daughter Zhuyin in her early age. At that time I avoid teaching her hanyu pinyin since she was learning phonics at that time. Teaching pinyin about the same time when the kids have not yet learn phonics should be avoided. But do not wait, Zhuyin is a good tool to use at that time.
See also: Zhuyin or Pinyin?
There are good Chinese input system that supports hanyu pinyin. My recommendation will be the sogou system.
