TM,
You certainly don't have to look far to realize that our problems are not so big in the scheme of things. I'm so very sorry for the hurt this little girl must be having to go through -and not to be cliche-but at this time of year I think it makes it doubly hard to understand.
That being said? I would do a little research (Mother to her Father) and have some information ready for after the holidays on where to go to help deal with grief as a child. Doesn't have to be spelled out - just maybe some suggestions of reading, counselors, pastoral counseling, an invite to your church or grievance groups - and hand it to the Father and leave it at that. Maybe some articles you know to be good about dealing with grief and children that are excellent excerpts - short and to the point. He may/may not appreciate it being that he will be dealing with so much this may be something that gets overlooked as she (little girl) may try to be BRAVE for her Dad. You can word a note that says you have had personal experience so nothing was meant personally - just that you understand how difficult it is and thought it would help.
Another thing that may help would be to let the Father know - you and Duckie would be open to "sit" or have "play dates" if he ever needs them. That could be more of a comfort to him at this time to know there is someone else in their corner than anything. An extra loving hand or set of eyes to help. Just down the street if he needs.
As far as a memorial or gift? I have ALWAYS enjoyed planting trees for the birth of babies, and birthdays - and even memorials. To me it says "LIFE GOES ON". I think a tree wouldn't be too much of an expense if everyone pitched in. If it was planted in their front yard? The little girl could watch it grow year after years and it could bring her some comfort. A gift certificate and memorial service in the Spring with a dedicaiton would be lovely.
Again - SO SO sending prayers and hugs for your neighborhood.
The only other thing that comes to mind if someone wanted to have something done NOW? Is name a star after her - so she could always have her mother looking down on her from above. Have no idea what it costs...but I'm sure a clever TM could come up with a certificate and pick a star out of the cosmos. (nearly free) - Many thousands to choose from and you can find one available easily with a home made certificate.
HUGS