As long as you have worked the hours that Service Canada degree, you will be eligible to EI. Depending when you finish work, it usually lasts for approx 9/10 months after your last paycheck.
Having the baby in Canada gives you no rights. In fact it can be a problem if you want to leave Canada and you do not have the Canadian fathers permission. So, if you have to leave Canada for status reasons, it does not mean you can take your Canadian born child with you. If it was me, I would always have the child born in the Country of my nationality.
You can apply for an extension of your visitor visa, if you are not intending to re new your work contract and work after the baby is born.
But being a visitor, you have no access to health care and although your baby would be covered, you wouldn't.
Think carefully about this, should you develop post birth complications, your medical bills could be thousands.
I work in an Immigrant Volunteer Center. So many girls turn up for our help, pregnant or just given birth, out of status and owing $1000 of dollars. Their choice, the Canadian father wants the child, so as a citizen it stays in Canada, the girl owes $1000's, until she is able to pay that bill, she will never be allowed back to Canada.
There is nothing we can do.
Please. I urge all whom are reading this. Think very, very carefully before you get pregnant in Canada.
It is not the gravy train many of you have been led to believe.
