Hi A.,
I went through this with my daughter.
My son does it too now - he's 9 months but it started at about 7 1/2.
I do a few different things, depending on the time period I have - like to shower and get ready randomly or I have somewhere to be....
If my son is awake and I have to take a shower, I take her and he stays in the high chair.
I find that after he realizes I am gone he stops crying and only starts back up as soon as he has a visual of me - like walking down the hall upstairs to grab a towel.
I ignore it. I see with my friends that the more they cater to the child, the worse it gets, don't take that lightly. It can get really bad.
I have a friend who now not only can not separate from her son at all but he starts lifting her shirt to be comforted all day and he's almost 2!
He sucks on her boob all night long, my goodness the poor boy has no confidence or independance.
Just put her in a safe place and do what you need to do, the dishes, your shower, phone calls.
I also carried them quite a bit. But at 6 months they can start getting heavy. I think a little of both is good, moderation. Carry them at a certain time of the day or only for certain acitivty...
It will get better!
Just remember it is completely up to you to establish her confidence, she'll realize your coming back in the room after repetition and that her fit, as tyring as it is for her, is to no avail and they'll get shorter and less frequent ;) We're creatures of habbit.