M.,
It's so tough when you have things to do and a little one who needs your attention all of the time. As a parent coach, and a mom of 2 (6 yo and 2.5 yo), I completely know what you're talking about!
You know that hindsight is always a good thing. You're in the middle of this now, but a few months from now or a year from now you'll have that hindsight. I can offer you the gift of it now since I have been in your shoes as a stay at home mom who had 2 demanding little ones.
First, you can't spoil a baby. They are biologically built to want to be near you and to be close. You can't hold them enough. It provides security. Part of why your baby is whiny and demanding is because she picks up on your desire to leave her alone. Babies are really good at picking up on our feelings. They feel it in the tenseness of our bodies, our breathing, our exasperated looks and our short, abrupt, or sharp tone due to our frustration.
To provide a win-win for you and your baby, get a back pack (the Ergo is a great one!) and learn to put her on your back while you get the household tasks accomplished. If you're checking email, hold her in your lap or put her on the floor next to you.
Your baby feels insecure. Independence CANNOT be taught. It is developed. If you continue to leave her and get upset with her about her need to be with you, you will create a child who will become one of two ways:
1. Very demanding, tantruming, insecure, selfish.
2. Very detached, cold, and withdrawn.
At 6 months your baby doesn't want you to be with her, she NEEDS you. Wants and needs are not two categories for her. She is not manipulative. Manipulation is taught and children develop the skill to manipulate later on.
Please don't listen to the advice about how you can basically teach your baby not to need you. It is sick, uneducated, and not true. It is the modern American mother's ignorant advice for creating children who live in their heads and not their hearts.
http://www.noblemother.com