Before I played said quest, I told my follower to wait outside Raven Rock Mine and then I entered. I completed the quest and read the Black Book. When I was at the point where I could choose a Black Book perk, I chose the one that makes me do no damage to my follower. When I exited the Black Book, I came back to the point where I first read it. Surprisingly, my follower, Illia, was standing there as well, but with none of the armor/items I gave her, only her standard robes and spells.
I could reload from where I left her outside the Mine but I think the same thing will happen after I do the quest. Also, checking the wiki, I found this bug: "Her inventory is known to reset."
If anyone knows a way of completing the quest without her inventory disappearing, that would be great (because the Bloodskal blade is awesome!).