it depends if you're applying as a skilled worker or immigrant, you can bring them with you but if you want to make it faster, then it would be under temporary foreign worker and you have to check the validity of your lmo with the processing time of what visa you would be applying for. check it with the canadian visa office near you.
This is confusing. It's obvious the OP is a TFW. And the only one who needs to be concerned with the viability of the LMO is the applicant himself. He must apply for the WP prior to expiry of the LMO. The accompanying family members do not need to concern themselves with this as they will be "attached" to his work permit. He does need to be concerned with the Skill Level of the job. If it is low skilled (C or D) it will be much more difficult for them to accompany him at any time. However, if it is higher skilled (0, A or B) then the wife and child can apply to accompany him with the wife eligible for an open work permit and the child, depending on age, eligible for a study permit.