She won't be allowed to bring the pets on a temporary work visa/permit.
You shouldn't allow it anyways as her bringing the pets is risking their lives. There's a good chance the authorities will put them down once she lands.
On the bright side, my nephew went to Taiwan on a 1-yr work permit to work as an English teacher. (He had taught himself Chinese, both spoken and reading/writing on his own). The contractor extended his visa for another two years. During that time, he met and fell in love with a Taiwanese woman whom he later married.
Shortly after that he was recruited to work directly for a major financial house correcting translations of old documents to/from English/chinese, as well as creating new documents.
He is not only very well compensated, but his New Year's bonus is the equivalent of a few MONTH'S wages.
He is very happy in Taiwan with his wife, gets along fabulously with his in-laws, and I don't see him coming back to the US at any time in the future other than for his semi-annual visits.
His wife is fluent in several languages and works as a materials buyer for a design and fashion house. She travels quite a bit. Right now she is in Florence, Italy coordinating the production of raw materials.
My nephew will be coming back to visit in July. My niece, nephew's sister, is coming back home the day after I leave for a trip to KY to do horsey stuff, and leaving before I return. This was a last=minute trip on her part or otherwise I would've scheduled my trip differently.