Pet Transport from Shanghai to Changsha

I'm trying to find a good, reliable company that can transport my cat from Shanghai Pudong airport quarantine to Changsha (my apartment) in the very near future. I'm moving to Changsha and my cat will be in quarantine for either a week or a month and I'm flying into Shanghai with her in-cabin. I will need either a transport company for my cat in Shanghai to transport her to me or I will need to know my other options on getting her safely to me.

Best is to fly via a city in China that does not apply quarantine.

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