I've fed both fennel and fennel seed. I have more experience with the fresh plant, and it's usually the first thing I reach for if I have any digestive issues in my herd. I have a bit of worry about stringy pieces, especially in large stalks and bulbs, so I've been cutting anything stringy looking crosswise. The bulbs have more water and sugar than the leaves and stems, but so far it hasn't caused me any trouble to feed it.
It is easier to get sickly feeling rabbits to eat fresh fennel than the dried stuff.
As for milk production, I've seen some negative side effects mentioned from using too much fennel, including appetite suppression and a lowered milk supply. So yeah, careful of the dosage.