This is one BIG reason I didn't last very long with breastfeeding! I had postpartum depression issues as well which made getting no sleep at all made things worse and WORSE! I see nothing wrong with using a little RAW goats milk at this time. I think you have done a great job! Maybe replace one feeding right before bed with the goats milk and breastfeed the rest of the night....that way you can possibly get a four hour stretch with a good feeding. She may just be wanting to suckle for comfort! Im not one to push the paci but it did save my butt a few times. Alot of times they want to suckle for comfort!
I know how you feel...I have a three year old that sleeps with us and it's STILL exhausting because he's up under me 24/7. I think eight months exclusively breastfeeding is great. A little raw goats milk at night will NOT hurt anything. Just don't overdo it! The goal should be to try to give breastmilk until 18 months and the next best thing would be raw goats milk....but no longer than 18 months.