The expression "get on well" is used in North America but more commonly "get along with." In Canada and the United States "get along with" your sister, for example, is more common. I think that "get on well" with your sister, for example, is more common in the U.K.

“Get on well” with someone ……..means you don’t have any major disagreement and have a good relationship. How do you get on with your new work colleagues? Yes, we get on well ( quite well) . The opposite would be just negative. My mother-in-law and I don’t get on well ( don’t get on at all)

It means "do you have a good relationship with your sister?"