Can I apply for transit visa?

Hi I hold Australian passport. I am flying to & will arrive at Nanjing on 24 October 2013. Then I am leaving from Shanghai on 26 October 2013 to Korea and Japan on a Cruise tour. I will be back to Shanghai on 30 October 2013 and stay at Nanjing for another 10 days before I fly back to Australia.

Since my first stay is less than 72 hours, can I apply for one transit G and one three-month-single-entry L?