I have an airport change from Pudong to Hongqiao. Need to check out my luggage at Pudong?

As for your luggage checking-in, it is suggested to ask your airline company directly. Some company provide that kind of service, but some do not. Generally speaking, if you buy the air tickets from the same airline company, you can check-in your luggage from your starting point to your destination, otherwise, you cannot.
As for the transport, you can take Airport Shuttle Bus Line 1 to travel between the two airport. The shuttle bus operates from 07:00 to 23:00 (T1); from 07:05 to 23:05 (T2) every 15-25min. So you can certainly catch one upon arrival.