I agree, many times donkeys will kill goats, either because they are being territorial or even if they are playing. Donkeys play by grabbing each others necks and will often break a goats neck by doing this.
We have 3 miniature donkeys. When we got our first, before we could pick up the other two, he was very lonely. We introduced him to the goats (he had been around a couple of old nubians) and he seemed fine. We sat with them for a couple of hours a day for several days and they were fine. Then a week later my most bossy goat challenged him (raised up and tried to head butt him) over the hay pile, even though I had several different feeders available. He grabbed that goat by the neck and gave him a shake. He did not kill him, but could have easily. The goat was very sore and swollen for a while, but did give him more respect. We separated them unless we could be out there.
When the other two arrived, the donkeys had their own pasture and the goats their own. Occasionally when I am out there, I will let them graze together, but one of the others is quite territorial and will chase the goats if they get too close or bother him. He will also chase cats, dogs, etc if they come in the pasture.
Mini's are too small to guard, they can easily be taken down by a big dog.
The only thing you can do is try it and watch carefully. You should also have an area fenced off or in the barn with a small hole that the goats can get in but the donkeys can't. This gives them an escape route if the donkeys are being too rough. I would worry that either the mom will try to protect her baby from the goats or the baby as it is growing will try to play with the goats like donkeys do and hurt or kill them.
