Hi red rum ,
We did this a couple of weeks ago , and following problems related on this site, We sent my hubbie running over to carhire while the rest of us dealt with the luggage retrieval etc . This worked for us!!
Problems seem to arrive at the minibus shuttle over to the car hire area - certainly when we were returning our car on the 20th August , there were huge queues for the bus . It is not really that far - maybe 700 metres - so you could leave your luggage to companions and run over ! or if you have wheels on your case go for it to beat the queues .
It seems to depend on what time your flight gets in , and if there are lots of others arriving around the same time . We have had problems in the past trying to get taxis late at night from PIsa airport too.