3 years old is too young for a study permit. Once your child is 4 or 5, you can apply for a study permit. It will cost approximately $15K per year in tuition to send your child to a public school (more for a private school). For your child to be approved for the study permit, you will need to show that you have the $15K to pay for tuition - plus an additional $10K to cover living expenses.
No - you won't be able to work. You can apply for a TRV to visit Canada temporarily but won't be able to stay long term or live here while your child goes to school. You will have to find someone who is already in Canada (i.e. Canadian citizen or PR) who can act as a guardian for your child.
If you wish to work in Canada, then you need to secure a job offer from an employer in Canada and that employer has to obtain an approved LMIA so that you can apply for a closed work permit. Having a child in Canada on a study permit gives you no benefits and does not allow you to work.
