From qingdao airport to the hotel at Yanerdao Road. Can I go by taxi?

Yes, of course you can take a taxi. The cab fare would be CNY 70-80 in usual time.
Or you can also take airport shuttle bus line 701 to get to Institute of Marine Geology first. It takes around 100 mins. And the ticket fare is CNY 20 per person. After arriving, walk southeast along Jiangxi Road around 0.6 miles to find the destination.
Just choose the way you like.