Both of ours had something similar to this that they developed shortly after we adopted them. I'm not sure if the vet ever decided whether it was officially "kennel cough" or something else. I think the term "kennel cough" can refer to several respiratory/cough problems. Anyway, it lasted 3-4 months, and we went through at least three rounds of antibiotics for it. But they both eventually got better. He also prescribed a cough suppressant to help keep the cough under control. And he said we could use Children's cough medicines in very small doses for the cough, too.
About pneumonia - each time you visit the vet, he/she should listen to your dog's lungs with a stethoscope. They'll be able to tell if there is any fluid collecting in them, and if there is, then they'll probably do further tests to determine if pneumonia has developed. It never did in either of ours. The vet can also tell a lot just from listening to the dog cough and from taking its temperature.
One other thing - our vet put off vaccinating our boys for kennel cough (bordatella vaccine) until they were both healthy. They were close to 5 or 6 months old before they got it. I think it's really only necessary if your dogs are going to be interacting with other dogs - for example, our vet requires dogs who come in for grooming, day-care and boarding to be vaccinated.
Hope this helps, and hope Lexxie feels better soon! Just keep in mind that it can take a while to get rid of it. It's awful to listen to and watch her suffer through, but she'll probably have a stronger immune system for it in the end.
