What to do from landing at Urumqi airport at 18:05 and departing next day at 8:45 to Dushanbe?

You are eligible to the 24h visa-free policy. No visa is required. Just apply for a stay permit, and you can leave the airport. For accommodation, you can consider Tianyuan Hotel at No. 1341. It is located to the opposite of the terminal, so you can easily find it. It costs CNY 500-950 per night. You can book a room by dialing at 86-0991-7611111. Or, you can stay at the lounges at Arrival Hall, T3; Departure Hall, T2; Arrival Hall and Departure Hall, T1. There are clear English guiding signs for your convenience! :)

Thank you Lewis for the information. Very helpful. Unfortunately my China transit is 28 hours so I won't be able to make use of the visa-free stay. I didn't mention I arrive at Guangzhou first, then fly to Urumqi before leaving for Dushanbe. I'll now have to get a double entry visa as I leave Dushanbe via the same route through China to Sydney.
Regan

Yes, in that case, you need to apply for a double-entry tourist visa or transit visa.