I think this is actually very normal, though you're probably exhausted and ready for a break! :)
I don't believe in trying to force babies to "get used to" not having mom or dad around, during separation anxiety stages. (And this really will come and go!) Because this is such a natural part of infant and toddler development, and shows a healthy attachment to parents. That's a good thing- you've done a great job at making sure she feels secure and loved!
That being said, you can definitely be very calm and reassuring during her hysterics. If you go into the other room for a minute, talk to her so she can hear you. Calmly tell her you'll be right back, and don't be gone more than a minute or two. When you really need to get something done, put her in a sling or backpack. She'll get to be near you, and also see that you have a life that involves other people/things besides her! (But still be comfy and happy, literally attached at the hip.)
Many people will tell you that this spoils your child, and will keep her from becoming independent. But my son was just like your daughter, and he's now fiercely independent! (Almost 14 months.) I still carry him in a carrier when he wants to be close, but he can play for over an hour on his own. He checks to make sure I'm around, and then goes about his business. He plays with other kids and his toys, reads his books, etc. It's a joy to see him so happy and independent, but he still cuddles and wants to be carried too. The best of both worlds!
Try different things for your daughter. Every baby is different. But don't feel bad about carrying her a lot, or keeping her close. She really will grow out of this stage. Though she'll come back to it a few more times before she's done!
**Oops, I forgot to add one other thing that helped us! If you sit near your daughter while she's playing, but don't constantly interact with her, that will help too. (Read a book, do a crossword puzzle, etc.) Same goes for when you carry her around. She'll learn to do her own thing, while still having you there for security. Good luck!