I agree that it's uncommon for the funeral home to pocket donations, but the family is undoubtedly aware of that obituary and would have approved it. It could be that the family can't fully afford the cost of burying Katie, and has asked that donations be made to the funeral home to cover Katie's final expenses. I can see a funeral home doing that if they were aware of the family's difficult financial situation. It's obvious that Miller's is doing this funeral on a different basis than they normally would.
My father passed away several years ago, and the total cost including the casket, headstone, viewing at the funeral home the evening prior to the funeral, church services on the day of the funeral, funeral home services (such as flower arrangements and limousines), rental of a hall and catering of sandwiches and coffee at the hall after the funeral, ran very close to $10,000. That cost didn't cover the double plot of ground in the cemetery which cost about $4,000 IIRC.
And, that funeral was done relatively inexpensively. If we had purchased a more expensive casket and flowers, and better food by the caterers, it could have easily run to $15,000. But, I recall talking about that with my dad when I was young, and we both agreed that spending money on a lavish funeral for a person was a waste of money. The person on whom the money is being spent won't benefit in the least from the better quality wood in the coffin or the more expensive flowers. They'd have been better off to spend that extra money on themselves while they were still alive.