I am inclined to recommend a vet visit because....
1) History. Rescue animals history is so often unknown and there may be a condition that has been brewing but left untreated because it was was not fully manifesting (sub-clinical), the previous owner did not appreciate, could not afford to treat.
2) Age. I hate to say it but 9 is getting up there. It would be really helpful to have baseline blood work (CBC and chemistry panel) even if it turns up normal it can be invaluable in the future as well.
3) Duration. Cats vomit regularly which is of no real concern but dogs not much so. A few days without an obvious cause-garbage can raid for example-is not okay.
4) Cough. This may or may not be related but my first reaction was worms/heartworm, as it could explain both the cough and the vomiting (of course there are other things but rescue, vomit, cough it was my reflex thought)

With this recession and what vets charge you hate to go in if you don't have to. That being said you have a few "small" reasons that by themselves don't really justify going in (unless money is no object at all) but combined it seems a visit is needed.

I do have a few questions. In relation to eating when does the vomiting occur? What is being vomited? Water? Food particles? Any signs of exercise intolerance?

I will PM you too.

Please let me know how Millie does if we don't connect today.

love and hugs B