Having spent more than a dozen years living in East Asia, I can tell you that there are quite a few things that you ought to bring with you...
A decent can-opener. One would think that because China is the place where everything comes from that you could find anything you might need. And you pretty well can, except that in many cases what you get is of terribly poor quality compared to what you can get at home. They export all the best stuff and keep the bottom of the barrel for themselves. Unless you want something that looks like it came out of a World War 1 army duffel bag that was dug up on a mountainside in Turkey, bring a nice can-opener with you.
Full-size towels. Asians just don't use them, unless they're staying at a fancy hotel. At home, they shower and towel off with tiny little hand towels. If you don't want to do that, bring a couple because they're outrageously expensive here.
Over-the-counter medication. Asians don't use full-strength aspirin (ibuprofen, paracetamol, etc.), nor can you get stuff like Thera-Flu, NyQuil or Pepto Bismol here. These people really took the whole 80s "Say No to Drugs" advice to heart, and they normally just suffer through bouts of illness. The pain medication and cough and cold medicine on offer here is rubbish, so I'd stock up.
Pot holders. Few people in China have an oven - practically everything is fried or boiled, but you might want to pick up a small toaster or convection oven and if you do, you're going to need a pair of potholders. It's not that you can't get them here, but the ones available are designed for pots and pans, not for baking trays, so I'd invest in a couple of good ones - full-size oven mitt style jobs if possible.
Lastly, it might seem strange, but you can't get proper greeting cards in China. If you like to send your mum a card for her birthday, if you like to send tidings to family at Christmas, etc., bring a few with you because they just don't have them here.
And bring enough books to last you until you can get to a second-hand bookshop - there's more than one in Qingdao so you'll likely be able to stock up, but bring enough to hold you over until you can find one.
Good luck getting settled, head.