I was thinking of starting a new country on a different world than my original country. Would this country count towards my empire, say for lvl 7, or does it have to be on the same world?
A new country on a different world(providing you haven't been on that world before)should start you off at lvl 0. Any new country on the same world will be the same lvl and counts towards the empire.
In addition to what my highly respected and esteemed colleague stated, a country on one planet does not count towards the empire on a different planet. Empires on different planets are considered separate.
In addition to both my learned friends advice, I would point out to you that starting a new country on a different world, hence a new empire, will cost you an additional 30GC per real month to maintain.