Travelling with a small dog on board train

Is it possible to bring a small dog aboard in a purse carrier with me as long as it is quiet? I want to take the train from Guangzhou to Beijing but I plan to get off about every 6-8 hours to walk and stretch our legs and board the next train headed there every evening during its various stops until it gets to Beijing so that it will be less stressful for my dog. He basically can sleep while on board the train in his purse carrier and we would get off in various cities throughout the train route. I know the whole process will take at least week to get from Guangzhou to Beijing but I figured that may be best for my dog and we will get to visit various cities too. I don't want to fly from Guangzhou to Beijing because Chinese airlines will not allow pets to travel in-cabin even if they're under 5kg. So... is it even possible to take a small dog on board a train without he being subjected to consignment? I want to keep a watch on him 24/7. Thanks.