Yes, I've given doxycycline to my Quaker when he had an upper respiratory infection and was Baytril, recovered from the URI, but then got a gastrointestinal bug about a week after stopping the Baytril. Doxycycline is a strong antibiotic but works very well. It can cause an upset stomach though, some animals/birds/people handle it fine and others get sick from it. But it does usually work quickly and thoroughly.
What is prescribing the Doxy for? The reason I ask is that if he's prescribing it for the original issue that Layla was put on Cipro for then in my opinion it's a great choice and a great idea. I remember that I thought Cipro wasn't the best drug for her at that time, but I'm not a vet, lol, so I usually shut up and stop talking when I'm at my avian vet and just do what he says! But yeah, I think two rounds of Cipro is more than enough and something different needs to be tried, and Doxycycline is a good, generally effective choice.
If he's telling you to stop the probiotics because of her diarrhea I understand where he's coming from, but didn't she just start taking the Emerald supplementation food? I'm just thinking that the diarrhea or change in her droppings could easily be caused by the Emerald or any of the medications, etc. she's been given. They have very sensitive digestive tracts and it only takes a little change to get them out of whack. Generally speaking probiotics usually help diarrhea or gastrointestinal issues.
"Dance like nobody's watching..."