You do have 30 days to submit the passport, and then mine took just under 6 weeks to come back to me in Canada. But recently its been much faster.
If you get the PPR end Sept, early Oct, and her flight is at end Nov, that could be enough time. Thats a good 6/7 weeks. I guess you just need to wait and see how things play out. If she get the PPR nearer to her trip, perhaps she could submit it from Denmark and wait for it to be returned to her there?
There's not a lot you can do until you hear from London... just keep your fingers crossed!