Hi and welcome here! I think it's great that you are going on walks together. You MUST keep it light! No talks about your relationship. Do not bring up the house, and DO NOT tell her she looks hot! Keep casual, keep it light. I would probably mention the dog walk you're going on - she'll see that as GAL (without her). She may like that.
Me 36 Husband 35 D5 S2 separated: 10/29/07-present Served divorce papers 1/22/09 "When the world gives out beneath your feet, it is time to learn how to fly."