If I've understood things correctly, this particular item can be used to get an extra pet slot(?)

But I'm still wondering what would happen if you used the plushie, adopted a new pet and then abandoned a pet in order to adopt another, would you still have a free slot from the plushie or would you need to buy another one?

You would be able to keep the slot. That slot is there forever, BUT you must have a Gold Account active to be able to fill it.