I am so sorry for your loss. I have also been through the same loss, my mum dies in an accident so it was a case of here one day, gone the next.
The first thing is to allow yourself to feel however you are feeling (if that makes sense). As you know, your Dad is perfectly entitled (and expected) to feel a grief beyond all words, so let him, but let yourself feel angry.
Helpful advice I was given was "never ask why". It is so tempting to try to get to the answer to this question, but it has no answer, and only leads to more anger and heartache.
You will get to a stage where your grief is not overwhelming, but it is not a case of getting over it, it is a case of learning to live with it. That sounds pessimistic, it's not - I am mostly very happy now (several years have passed) but sometimes the grief (or anger) that is always there surfaces. In some ways that is good as you never, ever want to forget.
Just be easy on yourself, and those around you - pull together. I now have a closer relationship with my dad than I expect I would have had if mum had not died.
Xx