Dopship great question! I am happy to hear you are interested in expanding the list of countries you are selling to.
While the United States may be the biggest market in the world, it is also the most competitive. I've personally known many dropshippers who have seen success as soon as they have started advertising and selling to other countries.
As far as I know, there are no countries that explicitly prohibit dropshipping (that I have come across anyways). However, I would not suggest dropshipping to any countries that have extremely long shipping times. From my experiences, South Africa and some countries in South America have 30+ days shipping minimum.
Here is a list with 20 countries to try selling to. Looking forward to hearing about your results!