Ahhh....OK! Good to know!
I'm kind of suspicious that your Rottie may actually have Kennel cough (Bordetella, infectious tracheobronchitis).
Kennel cough is a highly contagious cough that is transmitted by saliva or through an aerosol when a dog coughs. With kennel cough, dogs have a cough that sounds like something is stuck in their throat, and after coughing a few times they have what is called a "terminal gag" which means that they sound like they are bringing up phlegm.
If you watch closely, you will often see dogs swallow after this final gag - they are in fact swallowing phlegm. Some dogs will even cough up a puddle of clear, whitish, or slightly yellow mucoid fluid.
Kennel cough is highly contagious so dogs that have this should be kept isolated from other dogs for 2-3 weeks until it resolves.
Most cases resolve without medications, but in some cases patients are put on antibiotics and/or cough suppressants.
Antibiotics are used in dogs who are at risk for a secondary pneumonia (very young or very old dogs, or those with a suppressed immune system).
Cough suppressants are used when the cough is so severe that the dog cannot sleep. There can be quite a bit of phlegm with kennel cough, and it is better that the dog DOES cough that up, rather than leave it in the lungs by suppressing the cough. However, there has to be a balance where it's possible for the dog and his human companions to sleep.
When a cough suppressant is indicated, I usually suggest people buy something that contains ONLY dextromethorphan. A pharmacist could point it out to you. It's a little hard to find as so many cough suppressants have many drugs in them. Read the label carefully. Two possible brands are Phenergan DM or Robitussin DM (the DM stands for dextromethorphan). The dose is 0.5 0 1mg/lb (so, 50 to 100mg in your dog - I would start LOW). More information can be found here:
Watch your dog to see if she is retching or gagging at the end of her coughing episode. If she is, or if she is coughing up puddles of phlegm, she likely has kennel cough.
The vaccinations are reasonably effective, BUT their effectiveness starts to drop after about 6 months or so. The fact your dog was vaccinated 9 months ago means that hopefully this will be a mild case.
I'll give you links to further information:
If she coughs up fluid that is green, or is blood-tinged, or she is lethargic or has difficulty breathing, then you should definitely see a vet.
Many dogs with Kennel Cough seem to have a sore throat and thus don't want to eat their dry food. You can soften it with warm water to make it easier to swallow.
Keep your dog isolated from other dogs for at least 2 weeks!
Keep her as quiet as possible - just out for potty breaks and back in.
Kennel cough usually gets worse for 2-3 days, then frequent coughing with phlegm for 2-3 days, then starts to slowly get better.
It is also helpful to walk dogs with Kennel cough on a head halter or chest halter, as a leash around the neck can pull on the trachea and start a coughing spell.
If this has been helpful, please "Accept" my answer and provide feedback. I will still be here to answer further questions!
The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would strongly advise contacting your regular veterinarian.
Best wishes to you and to your dogs! Fiona