Hi Hi, - or is it Ho Ho!,
I laughed so hard until it hurt.
Seriously, true that women don't have a mitzvah per se. However, the early commentaries point out that they in fact are performing a mitzvah by assisting in the fulfillment of the man's direct command to be fruitful and multiply.
One explanation I've heard for women not having a direct command that it would be sad, insulting, and painful for a woman to be forced to go through labor and bear children. Rather, the woman who God created and lived in the Garden of Eden was given a natural desire by the Creator to have children despite the pain involved. God wished that the world not be desolate - rather that it be populated - and therefore the people He created, including women who need to "labor to have children" as you put it, in fact were created "in tune" with this desire to populate the world by having children.
