Grad school

I am an American engineer with a bachelors degree, my spouse will have her bachelors in history in one year. Is it feasible for us both to apply for grad school in another country, graduate and then look for jobs in that country?

I would be looking at doing this in England, Canada, or Australia.

The benefits, it seems to me, is that it would be easier to get a job in that country, you have a higher education, and are more familiar with the countries culture.

This seems like an easier route than just looking for jobs with sponsorships.

Anybody do something similar? What are the downsides to this plan?