You should be extremely slow and cautious about this new relationship. A person who's just ended a relationship is at a high risk of ending up in a rebound relationship that isn't going to last, and it's complicated by the fact that you're both in the midst of getting divorced. I wouldn't say that the relationship is doomed by any means, just don't rush into anything serious too quickly. It's a very good sign that you were friends before and have known each other as long as you have. Starting out as friends can be very good for a relationship, but only time will tell if it's going to become long term or not.
It sounds like you know what to do...just take things day by day as you have been doing.