Panting is generally a sign of pain or discomfort in dogs. Because your dog is a geriatric aged girl, there are many things that could be going on: some sort of neoplasia (cancer), thyroid conditions, blood disorders and even liver or kidney disease can cause both the panting and the occasional coughing.
A quick x-ray to make sure there aren't any masses in the abdomen and some blood work to make sure everything is as it should be will help rule out or diagnose what your pup has going on.
I hope this helps.
As with most things, in this forum it's hard to give you a 'for sure' answer about what could be going on with your dog and the cough. There are actually quite a few possibilities that range from the simple to the complex. Some of the biggest offenders are:
**Some sort of heart condition, such as congestive heart failure (also known as CHF):
**Upper respiratory illnesses such as bronchitis: http://www.petplace.com/dogs/chronic-bronchitis-in-dogs/page1.aspx
**Allergic reactions to inhaled substances such as pollen or dust: http://www.sniksnak.com/doghealth/inhalants.html
**Kennel cough, which is most likely if your dog has been boarded or kenneled recently, or if your pup has been around a large number of dogs in a place such as a dog park. http://www.thepetcenter.com/gen/kenc.html
**Canine influenza is not well known currently but is slowly working its way into the mainstream with more and more dogs coming down with it. http://www.petplace.com/dogs/canine-influenza-virus-dog-flu/page1.aspx
**Having a dog that is older or that isn't covered by a heartworm preventative can also develop coughs: http://www.gopetsamerica.com/dog-health/chest-lung-conditions.aspx , http://www.canismajor.com/dog/cough.html
**Finally, it could be that your dog is having what is known as 'reverse sneezing', which is also known as collapsing trachea. http://www.missionmedvet.com/encyclopedia/tracheal_collapse.htm ,http://www.beaglebuddies.com/misc/reverse.html
The easiest way to know for sure which of these problems is affecting your dog is to schedule an appointment with your regular vet. They'll do all the necessary work-ups (which may or may not include blood work and radiographs) to diagnose which problem your pup is having and the best course of treatment for you to follow.
Of course, it goes without saying that if your dog is having difficulty breathing, experiences lethargy or you notice a bluish tinge to the lips, gums or tongue, you need to seek medical attention for your dog at once as this is a sign that your dog is not getting enough oxygen for some reason and needs to be seen by a vet as soon as possible.
As for the panting...I'm starting to think that your vet may be on to something...it sounds like she does the panting most of the time during something good (like feeding time) or when she wants attention...as long as it's not bothering her (she's not having a hard time sleeping or anything), I think if it were my dog, I'd just keep an eye on it for now and write it off to one of those random 'old dog' issues.