I think you have the angle wrong is all.

Ok so the payment is alot all at once. But if you were paying her on a monthly basis it probably wouldn't seem so much.
We pay to service our cars, monthly for phone and internet - none of these we can do without but if you paid those things upfront yearly you would question that too.

Do you get your hair cut on a regular basis? Use childcare, get a massage etc? Those things are spread over a year - add them up at once and it looks huge.

As you say, you love your doula so you really do know how much she is worth - dontcha?