My girlfriend will be visiting Canada for about a month. Should we get health insurance? Is she covered in Canada?
Insurance is about trading risk. If you feel it is needed to avoid worrying, then make sure she has some.
Canadian public insurance which varies by province is based on residency and so it is unlike that she will be covered by it. In Quebec for example, you have to reside 183 days per year to be covered. The rules are rather complex and there are exceptions such as while studying abroad.
She may be covered by insurance from the US already. There is usually a clause in health insurance that covers someone for a certain number of days outside of the country. It is usually a few weeks but that depends. Read the fine print of her insurance plan. Some credit-cards also add travel insurance, including health, when buying the full-price of the ticket with that card. Again, read the fine print.