It doesn't look like she would qualify, since she wouldn't meet one of the four eligibility requirements:
Residency in Newfoundland and Labrador
The Newfoundland and Labrador Medical Care Insurance Act defines a resident as a person... "who makes his or her home and is ordinarily present in the province... ." Beneficiaries who establish residency in another Canadian province, must apply for health care coverage from the province where they reside.
Eligible applicants can be classed into four groups: Canadian Citizens, Landed Immigrants, International Workers and International Post-Secondary Students. The Medical Care Plan (MCP) requires documentation which must be provided by the applicant to prove eligibility under the Plans.
Also, unless the rules are different in NL...the OP would need to first be sponsored for Permanent Resident status by her boyfriend, after they have lived together for 1 full year (to apply as his Common-Law partner), or get married (to apply as his spouse) to eventually qualify as a Landed Immigrant. After becoming PR, she could work towards obtaining Canadian citizenship (but the law is changing in July, I believe, that requires 4 years of residency to be eligible).