Not much. The vaccines are pretty much same (at least in Ontario). Do get a vaccination history from current doctor before you move here, that way you can show it to your doctor here and they can give whatever is necessary according to schedule here.
My kid is not on PR. He is US citizen so he is here with his passport (which is considered as visa, I guess). He is not eligible for OHIP just cause he is our child. Good thing is, you can apply for PR pretty much immediately when you come here. Also, you can get OHIP once you apply for PR and they acknowledge that you have valid grounds to get PR. You dont need to wait till you get PR. Check this link : https://www.ontario.ca/page/apply-ohip-and-get-health-card#section-2
Another thing to note is, I came from US, and was always worried about medical expenses when you visit doctor. Here, even without OHIP, healthcare is affordable. Each normal doctor visit is $50-$60. And without OHIP, vaccines are still covered by government, so you need to only pay for doctor visit, not actual vaccines. So that cost us just $60 for getting him 1 year vaccination. We had to visit doctor couple of times for regular cold and such, which was same as well. So you can easily get by till you get PR by just paying out of pocket. One more thing I was told by doctor’s office is, that I should hold on to all the receipts for those $50-60 visits, and I may be able to get reimbursed for those once my son gets PR. He still haven’t got it, so I cant say that is true for sure, but something I heard.