Am I eligible for a 144 hour entry visa exemption?

Hi,
I am doing a backpacking tour in Asia with multiple stops and have a EU passport. After being in Indonesia and Thailand, from Perth I will fly on a layover in Kuala Lumpur to to Peking and then from Peking to South Korea. The itinerary is Perth-Kuala Lumpur-Beijing-Seoul. Am I eligible for the 144 hour visa exemption? Someone on tripadvisor said I should check with the embassy because all of my tickets are separate? Thanks for your help.