As a citizen of Lebanon, you would need a visa to visit Canada, see http://www.cic.gc.ca/english/visit/visas.asp?country=Lebanon
Regardless of your travel plans, return ticket etc. you are normally given up to 6 months stay which you can apply to extend as well if you want to stay longer. It is of course up to the immigration officer how long they give you, they can give you less time as well when you enter but you can still apply to extend.
Giving birth in a hospital in Canada can cost anywhere from $3000 to tens of thousands of $ if there are complications. If you give birth at home with a midwife, the cost is less and you can still send for an ambulance and go to hospital if there is a complication.
Keep in mind that having a Canadian child will give you zero rights in Canada. Your child could however go to Canada to study or work when they are older.