PUCCI, you're flying Iberia. I think need to sit down for this
I bring good news. One thing I love about Air Nostrum flights is the ability to drop off your hand baggage at the steps of the aircraft just moments before you board, and on arrival collect them on the way from the plane to the arrival gate. You sit upstairs in the cabin, and your cabin bag is safely stowed below in the very compact hold. Avoids all the faff waiting for the bags to appear on the reclaim carousel. Technically, we are permitted one carry-on bag but in practice, when I've had two, the lovely gate checkers happily gave me tags for both. That covers the basics but I confess doesn't remotely address your question about your wee animal. That said, i note that Iberia does not permit the carriage of weasels ferrets, pine martens, etc. but there is some info
here about less scurrilous beasties that might be of help to you.
As a BA Gold card holder, you'll have all the usual lounge benefits. I'm told the mushrooms come from a
tin barrel but I swear they taste better than anything that comes from my kitchen.