I should have been more clear.
I am currently inside Canada. My fiance is in India and does not have any visa.
My long term plans are to get Canadian Citizenship while on H1B and then relocate to the US. I am currently staying at a border city and was traveling up and down the border for work prepandemic. Right now I am working from home from Canada.
To bring a spouse from India to Canada.. it looks like it will take a year???
On H1B to the US it seems to only take a few months.
I am not sure why are you not checking the eligibility on both routes first. You have to consider the rules on both sides before you can decide.
There is widespread delay in interview schedules among various US consulates hence not sure if its going to be months or more than that.
If you are in US then you cant sponsor PR but can process H4. You should be married first, before you can even think of H4.
if you stay in Canada then you cant sponsor H4 but can process PR. You should be either married or prove 12 months stay with the partner for sponsorship.
First get married. Apply for PR.
Applying H4 quickly will resolve bringing her to US(after you move to US) but "after then what" should be your question if you decide US route. Later you end up not able to sponsor PR and you would then later think of moving to Canada alone to sponsor all over again.
While staying in Canada, one cant get H4 approval.