Is it safe to use oregano oil in a vaporiser for a baby?

Yes: Non toxic, even if applied in small amounts. May be no benefit. All the best.

I never would: I find that any fragrant material added to vaporizers actually acts as air pollution and often triggers cough and nasal congestion in small infants. While you may fine the fragrance relaxing, the babies nose and airway is very different from yours. Plain water is the best material, along with liberal use of saline nasal wash to clear babies nasal passages.