The average temperature of December in Shanghai is about 5 degrees.It's not a good time to take your baby with you.The best time to visit Shanghai is March to June and Septemper to November.I think .

The temperature in Dec. may be about 2~11C. It is cold but if you prepare warm clothes for you baby, it still can be tolerant.
Shanghai Tour(https://www.travelchinaguide.com/package/shanghai.htm) includes many good tour routes and some other usful information for trip in Shanghai and its nearby cities. You can also see the Best China Tours(https://www.travelchinaguide.com/tour/best-china-tours.htm) which provide advisable and good itineraries of travelling in China. Refer to it to make you trip plan. Wish you a good time in China.