Fist of all, you must realise that Girona airport is NOT in Barcelona, nor is it close to Barclona, even if some flight companies say so. Girona is about 1 hour by car from Barcelona.
There different routes you can take in order to get to Andorra from Girona.
Many route maps tell you to go via Olot, Ripoll and over the Toses pass which is the shortest route but by no means the fastest!
Take that route if you are on a motorcycle but not if you want to get to Andorra easily and quickly without having to go over any passes. You will probably have had enough of traveling by the time you get your car. As you still have over 3 hours of driving to do, the quickest route is best.
The route described below is the one taken by the bus that goes from Andorra to Girona every day and goes via the new Eix Transversal road.
Girona airport - Andorra route map