I'm no expert soldier, but I think you did fine with your conversation. My only comment would have been to leave this out: "I would love to share some with you sometime". So now when you have lunch, don't bring that up, let her. If she's interested, she will, and if not, that's okay too. Your dogs have picked up on your changes and she will too, even if you don't verbalize it. And it is actions that speak much louder than words and actions are what she'll believe.
I do find her opening statements interesting. I'm not sure she likes that from you and may try to draw you into something. I think you should stay with the 'giving you space' and 'not pressuring you'.
I know it is hard to manage those expectations, but lunch will not be the resolution of things, but it is a good step forward. Do you keep a log of small accomplishments on the road to your goal? This is certainly one that'll be on that list.
And I like #4. Given your lunch update and some things going on with me, i'll submit:
5) Learning patience.
me: 45 W:45 M 20 years T 22 years S14, S13, S11, D9 BD 2/28/14 D papers served 3/3/14 I moved out 3/15/14 MC start 4/2/14 I moved in 6/2/14 D suit withdrawn 6/30/14