A.,
I like Kathy's advice about inviting your baby to go with you! First of all, I would remind you that this is a stage, and it will pass. You have to wait it out; you can't force her through it. If you handle it well, she will come through this stage as a secure, trusting toddler, ready to venture out on her own.
I think the key is to understand that independence develops naturally when baby feels safe and secure. You cannot make a child become independent by pushing him away. Instead, baby learns that you are going to leave him soon, so he becomes hypervigilant for the next time you leave. Instead of becoming independent, he becomes anxious and clingy. Sometimes it's even worse. Baby learns that you aren't going to be his safe place, so he gives up on asking you for it and goes looking for it elsewhere. When children learn that mom will be there whenever they need her, that they can always come back for a hug and some safety, they develop the confidence to venture out. The best way to foster indepence is to be that secure place for your daughter whenever she needs it.
I kept both my girls close throughout their babyhood. They were both fed on demand. They slept in our bed for the first few months. My younger daughter lived in her sling the first 4 months or so of her life. Whenever we went out, they were in their sling rather than a baby carrier or cart basket. I was constantly warned that we would develop emotionally stunted kids who couldn't do anything on their own. Quite the opposite! Now my friends who wouldn't let their children anywhere near their beds, who made them play by themselves and left them with sitters when they were a month old, they are the ones with whiny, clingy children who are constantly on the lookout for the next time their parents leave. My girls run out and do their thing. When I get back, they are happy to see me, but they love to explore. My youngest, at 18 months, still cries when I leave her, but she stops in just a couple minutes and then plays happily. Both my girls play on their own without complaining. (Although I wouldn't trust the toddler without supervision!) They still need to be held and rocked and cuddled sometimes, but the vast majority of the time they are ready to take on the world. Remind yourself each time you hold your baby that you are building the foundation of independence. Just like she has to learn her numbers before she can learn to add, she has to learn security before she can learn independence.
You may find that you are more ready to meet your child's needs after you get a break. Can you get out on your own? Can you leave your daughter with Daddy, grandparents, or a regular, trusted care provider. My youngest used to cry horribly when I dropped her off in childcare or left her with Daddy, but within minutes she was playing happily. If this is the case, then try to get some time to yourself. Tell your daughter that you will be back soon, kiss her goodbye and then go. When you get home, remind her "See, Mommy always comes home!" Go see a movie, or do some shopping. Even a trip to the grocery store without a kiddo in tow can feel like a luxury. However, if your daughter cries the whole time you are gone, then she isn't ready yet. I would not leave my child if that were the case.
The best advice I can give is to watch how your daughter is responding to what you are doing. Respect the way she feels, and realize that her needs are just as valid as any adult's. If you meet her intense need for you now, it will be satisfied and eventually she will grow out of it. If you try to force independence, her need will just get more intense, and she will be stuck in it. Follow your child, follow your heart. Do the best you can, forgive yourself when you fail, and that's all you can do!
Best of luck,
S.