Firstly my heartfelt sorrow for the loss of your father, I can hear how very very special he was to you and how much you love him. It is so very hard when we lose someone we love and even more so when we have had to go through such a traumatic experience as you have with his cancer and treatment.
Secondly, congratulations on your upcoming wedding, it is going to be a day filled with so many emotions for you and your new husband and child. In your heart your father will very much be with you on the day and you think of him. There are so many ways in which to grieve, there is no right or wrong way, so when you said "I haven't grieved as you should.." you actually are grieving, in the way that you need to. There is no time frame and there are no rules, your father will live in your heart and in your memories forever, there are no rules to say that you must visit his grave, you can do that when you are ready to, and you may never, it is up to you.
They say time heals, I am not sure that it does, just in time things become different, and you have a new way of living now that your father has passed. Hearing songs and smelling smells and all these sorts of thing evoke our memories and that is totally fine that you get upset, you love him very much and it will take time to be at peace with it, afford yourself the time to cry and the time to heal, without limits or expectations on yourself.
You will miss the presence of your father physically on your special day but as I said before, he will be with you in your heart on the day. There are lots of different ways that you can include your father on the day if that is something that you wish to do too, I am sure you have thought about it a fair bit. Once again, there is no right or wrong way, you do what you would like to on the day to bring you peace and so that you can enjoy your day with your partner and child.
Big hugs to you and I hope I have given you some comfort today, I would like to chat some more if you would like that too.