Sunfish, losing your Dad is a really sad time and I hope you and those close to you bear up all right. You are very wise to follow your own mind and give yourself some time to get over it. Unless there are other reasons though, I don't think it's an aviation doctor problem unless you can't sleep or concentrate or similar.
In my case, I was travelling in the country in the plane when the news came through that my Dad had passed on. Fortunately another (non-pilot, but GA-friendly) family member was with me and after some thought we agreed that I should fly back and he would come with me. We decided that the only safe way to do it was put everything else out of our minds for the next few hours and fly this trip just like any other. That's what we did, and had no difficulty... But I don't know if I would have done so as easily on my own. The other travel options weren't at all practical and the weather good so it really wasn't a difficult decision. The flight went without a hitch and I am confident I would have been quite OK at dealing with anything untoward that might have arisen. If the factors were different (unfamiliar route, weather, aircraft issues, etc), then I may well have sat out the day and worked out some other way to get home. We did not discuss Dad or any of the related matters during the flight; that might sound heartless but it seemed better to me to save the emotion for later on. Having helped me get into aviation in the first place, he would not have wanted me to fly that (or any other) trip anything less than professionally anyway.
The part I didn't handle so well was the funeral a week later and the day or two either side of it. I gave the eulogy at his funeral and even preparing it was stressful. I had nightmares around this time as well and passed on flying for a week or so afterwards.
I think the right response depends on how you feel and whether you are confident about your judgement and state of alertness. If there's doubt, give it a rest, but when you feel ready, put your mind to flying and everything else aside for a time, as you always should anyway. You might find that taking the next flight with a friend who also flies will help. Doing something you're good at and enjoy, as long as you're safe, won't hurt you.
My suggestion is to take it all one or two days at a time for now. It seems this type of grief affects different people in different ways. You'll know yourself when you're up to it, but don't rush it or be impatient with yourself. Best wishes in this difficult time.