Getting your MD to order the tests should not be an issue. The issue will be getting your insurance to pay for the tests since you won't be getting them for any specific symptom.
You should know that one test will not tell you much as T levels can vary from day to day.
You would need an average level from 3 tests done at the same time of day (early AM) to approximate what your levels are.
Things like calories, sleep, stress, drugs, and alcohol can effect T levels so there is a lot of variability.
I think you would get more bang for your buck getting your C-Reactive Protein levels and Liver function tested.