Congratulations on the pregnancy! I contacted my doulas just in the beginning of the 5th month, and although they did mention that it was kind of early, it also sounded like a lot of women due around my time (April) were contacting them early, too. So I think it tends to go in waves, so earlier is always better, as you just never know.
I also felt a HUGE sense of support and relief in hiring them relatively early, so you might find that the process of hiring a doula feels good. And if it feels good, do it!