Ah yes, I should've clarified further but got lazy ;) I included the first paragraph to add context as follows:

I looked at her and it felt as if the sun had just come out.

This sentence focuses the action on two characters, the narrator and the lady. So in the next paragraph, it's not clear who is speaking and using 'she said' could be useful.

“I tell you what," she said playfully caressing the puppy. "I’ll take the mutt home with me, but you’ve got to agree to come over to my place and visit..."

On the other hand, if the preceding paragraph had focused the action on a single character, then 'she said' might not be necessary.

The sunlight streamed through the window, and she looked at me with bright eyes.
"I tell you what. I’ll take the mutt home with me, but you’ve got to agree to come over to my place and visit..."

In this second instance, the action is focused on her, and so further clarification of the speaker may be not necessary. Less is more in this case because fewer words give vigor to one's writing.