Emergency plan for Minor

Let's hope nothing will happen to you. In the worst case scenario your plan looks sufficient.

Suggest that you contact someone at the American Embassy in Beijing in advance of your trip, and perhaps arrange a face-to-face meeting while you're there in order to establish a personal contact in the event of a worst case scenario. Might provide some peace of mind for you both.
It was always standard practice when I visited there on business to have the hotel provide Chinese language instructions on a business card or slip of paper to be able to show to a non English speaking cab driver in order to get home again.

"...the embassy staff will have more important things to do than meet a 12 year old just "in case" there is a problem. :-)"
Actually, part of the mission statement of the American Citizens Services (ACS) section at the Embassy is to provide these types of services on request. Might add as a personal note that everyone I ever met with at the Embassy, or the Consulate in Shanghai, was extremely kind and helpful - the kind of people who would probably be happy to stop by your hotel one afternoon just to say hello and connect a face with a name.
Might indeed be overkill, but for your peace of mind you should know that the service is available to you if desired.

I made sure my daughter had a charge card for emergencies. If all else fails, she could get a room and/or buy a ticket home. Also, I made sure she had a complete itinerary with hotel addresses and telephone numbers. We also had a system if separated. You'll have great fun! I loved traveling with the family, but also traveling alone with my daughter. The chemistry is just different between the two types of vacations, so that was fun. Wray

"Beijing is one of my favorite places that I have ever visited."
Mine too, Emma, and for all of the reasons you state. Probably the biggest case of Culture Shock I've ever experienced... but in a good way. Hoping to go back one day.

...and the number for the company providing our guides....

Since you have a agency providing guide service, provide the agency with emergency information such as:
Emergency contact information (Legal guardian)
US/domestic medical insurance carrier/policy number/telephone
Travel medical insurance carrier/policy number/telephone & medical evacuation plan

Have child carry local contact information (China guide service, local hotel) including a hotel card. It seems almost everyone in China carries a cell phone.

hka,

As you appear to be travelling alone with your daughter, it may be prudent to get a notarized letter signed by the other parent, which states that you have permission to travel with a minor child on your own. Authorities in many countries are starting to check for that, due to the incidence of child smuggling.

Your profile doesn't indicate where you're from, but this is the information from the Government of Canada on that topic. Your government likely has similar information.....

http://travel.gc.ca/travelling/children/consent-letter

Thank you everyone, good ideas!

I have been to the American Embassy in Beijing and it is, quite literally, a fortress! I only was able to go inside because I was in China on a diplomatic visit through the US Dept. of Education and, even then, I was not even allowed to move freely in the building. It's quite a place.
That said, they will help your daughter if, God forbid, something happens to you. Here is the information she will need. Don't be worried about being in China with your daughter by yourself. It's a wonderful country with many modern services! Have a great time!

"I have been to the American Embassy in Beijing and it is, quite literally, a fortress!"
I think you'll find that heightened security is the order of the day at all of our overseas embassies. The only area you can access without an escort is the ACS. That's why I suggested making contact with a representative in advance of the OP's visit.