If you move a WoW-license to a new/separate Blizzard account, the following will be moved/ not moved:
Will move |
Will not move |
Game account and expansions |
Unused character boosts |
All characters and their inventory, bank and void storage |
Items in the Collections Journal including mounts, pets, toys, wardrobe items, and heirlooms |
Character-specific achievements |
Account-bound achievements |
Gold and other currencies |
|
Game time |
|
Regarding pets being linked to achievements - I believe that once you have earned the pet the two are completely seperate (achi/pet).
Source:
Combine Blizzard Accounts - Blizzard Support
Although the article is about combining Blizzard accounts, the bottom part speaks of transferring a WoW-license to a new Blizzard account if it happens that you have filled up 8/8 WoW-licenses on your main Blizzard account (scroll down and choose World of Warcraft under "Select an option").