I always look to the obvious first, before trying to go into too much depth. Had you seen pics of your dad recently? Been reminded of him in any significant way? What date is the date he alluded to? An anniversary of some sort? Even that little exchange could have been something you saw on TV or in a movie. If you saw a pic of your dad, and then heard or saw someone on TV or elsewhere talking about something happening in a week, or falling ill and dying within a week, it could simply be that. Last night I had a crazy dream about a girl being locked in a dungeon-like room, and wondered where in the heck that image came from. I remembered I'd just watched the movie Quills again, and many scenes take place in a dungeon.
It could also be completely subconscious, and could have something to do with wanting to be closer to the rest of your family. They were in the dream too, and you were all sharing an experience of loss. Death is horrible to endure, but it can bring people closer. Maybe you should ask yourself what you'd have done if you knew your father was going to die. It could simply mean that you need to rekindle a bond with your family. You felt sorrow, but did you feel anything else? Did you feel blessed to know this in advance? Did you feel especially close to your family? If it was only grief that you felt, it could also be you expressing regret that you didn't know sooner. There are a lot of possibilities. I always ask myself what EXACTLY I felt in the dream. I think most important, even beyond the action taking place, is how the action is affecting you in your dream. The key points of your dream I think are that you and your family found out in advance that someone you loved was going to be gone soon, and you shared your feelings with each other about that.
Good luck to you in figuring it out. Hope you get some helpful direction on here.