The Apple AirTag is primarily designed to help you locate a misplaced item. It does not perform well as a tracking device, whether it is for tracking pets or people. However that doesn't stop folks for using them for this purpose. You will even find third-party sources that will happily sell you pet collars that can hold these tags.
As muguy has already mentioned getting a location update will be sketchy at best for a number of reasons. Primarily based on how these tags work within the Apple Find My Network.
If you goal is to keep track of your cat, you should consider getting a dedicated tracking device, that is based on GPS, not Bluetooth.
If you purchased this AirTag, directly from Apple, you have 14 days (from the purchase date) to return it for a full refund.