No, you're not on the right track. Think of it from the dog's point of view...mommy picks me up, I growl ( I don't like being picked up), mommy punishes me (more reason not to like being picked up). In fact, I'd reconsider all the reasons why you're picking her up. It's quite possible she's associated being picked up with many different negative outcomes. Baths, being restrained on your lap, being brushed, nail clipping...all these things dogs have to learn to tolerate. If they haven't learned to tolerate them, her behavior will show it when you pick her up.
So, why are you picking her up? Do you need to? Can you work around not picking her up? I'd start there.
If you must pick her up, give her a reason to enjoy it. Start with short pets, and follow it with a game, or a tasty treat. Progress to longer touching and even more awesome rewards. You need to change the association before expecting the behavior to change. She is warning you for a reason, and if she hasn't bitten you, it's a good time to resolve why. Growling isn't abnormal behavior, irregardless of the context. She has reason, now find it.
So, why are you picking her up? Do you need to? Can you work around not picking her up? I'd start there.
If you must pick her up, give her a reason to enjoy it. Start with short pets, and follow it with a game, or a tasty treat. Progress to longer touching and even more awesome rewards. You need to change the association before expecting the behavior to change. She is warning you for a reason, and if she hasn't bitten you, it's a good time to resolve why. Growling isn't abnormal behavior, irregardless of the context. She has reason, now find it.