I would say that her political philosophy was simply Americanism, based on the principles of the Declaration of Independence.
All men have the right to life, liberty and the pursuit of happiness and this was the essence of her political philosophy.
She rejected any philosophy or relationships that would make the individual a slave to someone elses goals and ends.
Interesting point, and true enough.
The US declaration of independence makes assumptions that are not necessarily obvious, even if they are ascribed to God. Other people with different traditions, and as great a belief in God, have come up with different ideologies.
Libertarianism - the idea that individual liberty is central - was pretty much a foundational piece of American culture, so native that the natives had trouble noticing its presence, and the degree by which the US was unique in the world. If you are a fish, perhaps, it is hard to notice the water.
Foreigners however did notice. Which is why I think all the first writers on libertarianism as a political philosophy were not American.