I find it awfully odd to use logistic regression since income is clearly not binary. Sometimes people use logistic to explore if people are in the "top X%" or other sorts of ad-hoc quantile regression. Using logistic seems sub-optimal to me, but perhaps passable. I would prefer quantile regression.
If everyone is employed and you have no unemployed doctors, then you have a wide range of incomes, it makes sense that the distribution would be approximately log normal. Income distributions have heavy(ish) tails. This is commonly held belief, tied to "Gibrats Law".
Here's an interesting paper on it- carefully note they chose to argue more log normal than. It implicitly confesses of the widely held belief that both consumption and income is log normally distributed. There are probably more basic papers, but JPE is pretty respected and this has 100+ cites and a good place to dig.
Battistin, Erich, Richard Blundell, and Arthur Lewbel. "Why is consumption more log normal than income? Gibrat’s law revisited." Journal of Political Economy 117.6 (2009): 1140-1154.