I'm so sorry, that is so very young to lose your dad. I understand what you're saying about your age relative to the loss. I think it's very natural and justified. I had similar thoughts and feelings.
You won't continue feeling this bad. Those days when the pain feels unsurvivable will gradually reduce. You won't notice it's happening at first, but it will. I promise you it gets easier to bear.
I think you are coping, it's just that what you're coping with is huge. Grief is painful and takes a long time. It's not like in popular culture where you cry a little bit at the funeral and then have "closure" and away the grief goes into a neat little box never to be seen again. There's a lot of pressure in Western culture to grieve in an unnatural emotionless way that doesn't reflect how humans actually grieve. It takes a long time.
What you're feeling is normal - please don't feel you're grieving incorrectly or that there's something wrong with you for having these thoughts and feelings. You're approaching the first anniversary and that can be difficult - there are points where the shock fades and it starts to feel real that this is permanent. I had those feelings, others have had those feelings, you're not alone in struggling with the realisation that he really is gone.
One thing that helped me was to understand that our relationship with someone doesn't end when they die. It changes because they're not physically present, but it doesn't end. You don't have to try and box away your dad and leave him behind as some sort of neat parcel of grief - you can carry him with you throughout the rest of your life. He has shaped the person you are and the person you'll be in future. You can revisit your memories of him, you can ask yourself what advice he might give or what anecdote he might share in different situations. You can talk out loud to him if it helps you. In future when the pain is more bearable you can talk to others about him. You can continue to bring him with you.
He's not physically present anymore, and for that I am so sorry, but your relationship continues and you can continue to carry him with you in your life.
If you haven't had any contact with bereavement organisations, I would encourage you to explore any support they can offer you when you feel ready. In particular, there's Cruse, Sue Ryder and Marie Curie who all have different types of bereavement support available to anyone.
And please don't give yourself a hard time for how you're feeling 💐