"it's not my place to cry in front of those who have more right to be upset" - I understand what you mean but don't agree. Crying means that you loved him and will miss him, there is not a scale of grief which is measured by the amount you cry. Some people grieve deeply without being able to cry at all, its more a function of your personality and upbringing.
I agree it wouldn't be appropriate to sob and wail over his daughter about how upset YOU are but it is entirely appropriate for her to see that you loved her father enough to shed a tear in public for him. At the funerals I have been to, dearest and dearest have been very touched when people have cared enough to cry.
Agree it would be a nice gesture to take her something - you can say that you understand that she won't feel like it just now but you have brought something she can freeze. Also a good idea to split it up into portions if you can.