Have you tried a sling carrier? They make them for toddlers (not just newborns), and REALLY help out when you want to get things done, but your child just wants to be close to you. They allow both of your hands to be free while still having the child up against you, so it helps out if you need to cook, clean, etc. It took a few days for my child to get used to it (we have a "Snugli" carrier... not sure the weight limit though on it... Try googling "sling for toddlers" or something), but now he loves it and it has really kept my sanity.
While the "ideal" may be that she is content being alone, or at least not attached to your leg, your child DOES need you right now and this is how she's expressing that need. It may not be fun, and it may be exhausting, but meeting this need right now with her will defniitely be a short term sacrifice for a long term gain. I majored in psychology in college, and the previous moms are right when they say that children go through stages of "mommy and me are one", "mommy and me are separate - oh no!", and "mommy and me are separate - yay!". It can be scary and confusing and different for the child, but the good news is that it doesn't last. She will eventually realize "oh, mommy and me can be separate, and it's okay. She's still here for me, I'm still safe and protected, so nothing really changes. Wow." Unfortunately it may seem like it's taking forever in your eyes, but it will pass. If you don't take the time with her now, then later on problems will most likely develop (i.e. dependency and security issues). Some children have an easier time realizing they are independent of mom than others - each is unique!
You might also want to begin reassuring your daughter verbally (in addition to physically) that you are there for her, that you'll always be there for her; that she is safe; that you and daddy are watching out for her and will do your best to protect her; that she is her own little girl, separate from mommy, but it's okay because you still love her just the same and are still there for her just as much; etc. You might feel odd saying some of these things to a 1 year old, but children understand more than we give them credit for... and it just might help her transition from "clingy" to "hello world, here I come" faster if she has that reassurance and confidence from mom and dad that she's still safe and secure no matter what.