Australia and Canada both offer a points based immigration system, which allows you to move to the country even without a job offer lined up.
For example Canada requires 67 points. You get 22 points for a university degree, 16 points for speaking perfect English (another 8 points if you're fluent in French), 21 points for four years of work experience, and 10 points for being between 21 and 49 years old. That's 69 points and enough to qualify for a visa, even without an employer.
Australia has a similar scheme. I'd say concentrate on your language skills, so your preparation for the TOEIC is the right path. I would try to find out which tests are accepted by the immigration authorities in these two countries and go for that.
The UK used to have a points based system, but that ended in 2010.
Good luck!