You indeed do not need any paperwork for merely transiting through DOH as the animal technically will not enter the country. However, you will not have access to the animal during the layover. QR will cater to her in an animal transit facility, where she will be taken out of the crate, given food and water and an opportunity to relieve herself (this partially explains the high prices they charge for AVIH animals).
BTW, this is just about the least favorable routing one could do with an animal. She'll be in her crate for about 18 hours from check-in at LAX until arrival in the DOH animal centre - I`d have gone transpacific.