The easiest way to find out if you are eligible is to contact the provincial healthcare directly to find out if you are eligible for their coverage. Basically my understanding is that you will need to meet certain requirements to become eligible (work type, amount of hours etc.)
Just contact them prior to arrival- here are some of the most important ones:
<a href=http://www.health.gov.bc.ca/msp/infoben/contacts.html>Contact BC MSP</a>
<a href=http://www.health.gov.on.ca/en/public/programs/ohip/>Contact Ontario OHIP</a>
Other provinces have dinky websites but I'm sure it's easy to locate.
A good idea is to get a plan that you can refund once you get your provincial coverage. In case there is a waiting period for government healthcare or you need 2 year insurance to get your 2 year visa- here is where you can find more info:
<a href=http://arbetovinsurance.com/iec-travel-insurance/>IEC/ Working Holiday Insurance</a>