There isn't enough time for your husband to sponsor your for permanent residency.
So if you want to give birth in Canada, your only option is to come here as a visitor. To come here as a visitor, you must apply for a tourist visa (temporary resident permit).
Since you will be a visitor to Canada, the birth will not be covered by the public health care system. You will have to pay for all of the costs of the medical appointments, tests and delivery yourself. I would budget $8K to $10K to be safe. The costs could be significantly more if there are any complications. You can also reduce the costs by using a midwife and having the birth at home.