Doulo isn't even a word.
A doula is a woman by definition. It's not a role, it's a person.
Like woman.
Although this article says there are men who perform the same job, called 'dude-las'.
blogs.babycenter.com/mom_stories/12052013-male-doulas-is-childbirth-womens-work/
The article points out some benefits to male doulas, including offering unique support to the laboring woman’s partner. It’s also possible a male doula could reduce the chances of the father feeling “replaced” or being made redundant, by the presence of a female doula.
I'm sure the concept of a doula is appealing precisely because it strips away modernity, and takes us back to a more primeval acceptance of female understanding and support.
It's not an equal opportunities exercise.