What can I do to get a genetic test done to determine if I am a carrier of the leukemia genetic mutation?

What test? What "leukemia genetic mutation" are you referring to? I am unaware of any screening test, where screeening is defined as testing in an asymptomatic patient. Need more info...
Not recommended. There is no single genetic mutation. Different types of leukemia are associated with different genetic abnormalities. These are multiple and testing for all of them is not reasonable from many points of view including medical necessity and cost. Genetic testing for specific mutations and other abnormalities is performed only after a diagnosis of leukemia is established clinically.

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How can I get a genetic test done to determine if I am a carrier of a leukemia genetic mutation?

No reliable test. There is no test like that. There are companies offering comprehensive genomic mapping etc- however, I would not recommend it as it is not primetime yet. There are a lot of questions in regard to that - ie. Not clear how reliable it is, how would you interprete the result, what is the consequency etc. It is for sure will increase your anxiety level. Discuss with your md in detail.