We, 2 of us, intend to fly into Beijing from Kuala Lumpur in early Mar '17 for a trip to Shandong,

You can take high speed train from Beijing to Jinan, the ride takes around 2 hours. From Jinan, you may take high speed train (40 minutes) or bus(2-3 hours) to Qufu. Then take bus to Tai'an (one hour) and visit Tianshan. From Tai'an, you can take high speed train to Qingdao (3 hours) and then take train (5 hours) or flight to Beijing.