I like the Benelli Super Sport in 20ga, has the comfort tech recoil system in it, its about 6.2 lbs ( so its awful light ), 28" barrel - and you can buy the optional left hand recoil pad ........ so I think its a good choice / and they are way easier to care for than a "gas gun" in my opinion.
Its the gun I train 2 of my 13 yr old granddaughters with - and they like it a lot. The synthetic stock is cool ....
If that isn't what you want / I would search out a Remington 1100, 11-87 or a Beretta 390 or 391 - that you could shorten the stock on - or buy a 2nd stock for it / keep the original for later as she grows.