It will be the hardest public speaking you will ever have to do, and if you tear up, and have a hard time with it, That's the way it is. I don't think people expect to see someone be a rock up there.
It's so hard to lose someone, but like you said, she's in a better place, she's not hurting anymore, and you can take comfort and solace in that. Focus on celebrating the life she led, not in her death.
The hardest thing I've ever had to do in a funeral was sing in a group a song called "Old Irish Blessing" which I never really saw the true meaning in until the funeral as I was singing it, and it is
SO hard to stay on pitch when your choked up. lol Thankfully it wasn't just me up there, I had another 7 people, and 1 more bass to help me out, but by the time we were done, there wasn't a dry eye in the house, but people were so appreciative of it, and it moved them so much, it was good for the grieving process, because it helped us see the hope that comes with death. Focus on the hope, and focus on the beautiful life that she led, her death is just the beginning of something even more amazing.
You'll get through this, keep your head up and stay strong. Good luck with the Eulogy, we'll be thinking about you.
Ben