How much if any of the properties of prune juice will pass through the breastmilk to a child? If I drink it in moderation will my daughter benefit?

Insignificant. It will probably not have a significant effect to benefit your infant for her bowel movements. You might hear of anecdotal reports of laxative effects, however, no studies have concluded connections with a mother's intake of prune juice and subsequently breastfeeding and later facilitating looser stools in infants.
Most likely none. If your daughter has issues with constipation, it will not benefit her if you drink it. You can try pumping and mixing in a small amount of prune juice and bottle feeding her that.