There actually could be several different reasons why a small dog like this might intermittently cough/gag which I'll list below.
If it's been going on consistently for more than a few days especially since she was recently boarded, I might also consider kennel cough which is going to be either secondary to a viral or bacterial infection. If this is a bacterial infection, then she should respond to antibiotics pretty quickly; however, if this is a viral infection, then it will have to run its course...which is usually about 10-14 days or so.
The other possible causes for this behavior when it's not constant but intermittent, though, include:
1. Bronchitis which is similar to asthma in a person. These dogs are reacting to something in their environment that triggers inflammation in their lungs. If this is the case, then control vs cure is what might be expected and the treatment is often different for each dog.
2. Collapsing trachea is primarily seen in smaller dogs and is pretty much what it sounds like. This is a manageable condition for the most part unless surgical intervention is done to correct the problem. This condition can sometimes be difficult to diagnose on an x-ray but is what I'll usually recommend if I'm trying to determine if this is the problem or not.
As to treatment options, much depends on the vet and the patient, but the following are things to consider:
1. OTC, human cough preparations such as Dextromethorphan can be given to dogs: http://www.petplace.com/article/drug-library/library/over-the-counter/dextromethorphan-robitussin-dm
The dose would be 0.25 to 1 mgs per pound of body weight 2-3 times a day. You just want to double check labels and ensure that the formulations only contain this ingredient although inclusion of Guaifensin is fine.
2. Use a harness instead of a collar.
3. Avoid any potentially irritating substances such as cigarette smoke or excessive dust.
4. When an episode is occurring, I'd also advise that you feed dry dog food (if this is what you feed) soaked in water for 15-20 minutes which turns the food into mush and is less likely to cause more irritation to the throat when it's swallowed.
Personally, I don't worry when a dog this size intermittently cough/gags as long as they're otherwise acting normal. However, if the condition is worsening or other signs develop (such as being tired all the time), then I usually suggest that an x-ray be done to evaluate the heart and lungs.
I hope this helps, Deb