Why does Kagami feel necessary to emphasize that she is a simple-minded person?
Kagami sees her simple-mindedness as something desirable

To explain a bit more, in that scene Tsukasa very innocently expressed her desire for a pet dog and didn't even consider the possible down-sides because of her air-headed character and the fact she was excited about owning a dog and single-mindedly chased after what she wanted. 

Now, Kagami's character throughout the series has been established as the more forward thinking of the two sisters, but she doesn't want to be! When she reacts this way it is expressing how she wants to be like her sister, she tries to stave off the comments about how responsible she is by saying that she was just the same as her sister and innocently wanted a puppy too! And she was only the voice of reason here because she had been enthusiastically and innocently thinking about it for a while.

Throughout Lucky Star, it is a running gag that the sisters both envy the others personality traits, and this scenario seems to be an example of that. (you can also see here how Tsukasa also wishes she was more responsible like Kagami)