New Mom, Baby Dry Cough

Keep nursing, it is better for her than formula. Breastmilk is very hydrating. Check her temperature, if she has a fever call the doctor. If she has no fever but the cough persists for more than four days, or is really chronic and preventing her from sleeping then call the doctor.
The weather down there is supposed to be getting back to normal (according to my sisters who are there), but a drastic change in weather may actually make her cough worse for a couple days.
Watch her and follow your gut, if she just seems "off" then go ahead and call the doctor, it can't hurt!

No one can give better advise than a pediatrician....call the office and ask :) If cough is the only symptom, there's not much you can do. If she's acting okay, then it's probably not bothering her.

Good that she wants to nurse. Your breast milk provides her all the nutrition she needs.

This can fall in the "usual" area.

I agree call the pedi.. Our child as an infant and toddler had this and ended up as asthma.. Of course they would not diagnose this for a long while. They need to make sure.

Consider getting a electric room filter. It really helps to get rid of all of the dust and allergens out of the air. Keep up with changing the filters.

It really seemed to bother and concern us more than her.

My daughter has milk protein allergy- her symptoms at first were rash on head (looked like heat rash) and a dry cough. At 1, when we tried whole milk, her only symptom was a dry cough. The pediatrician wasn't even linking it to the allergy, I just went out and bought almond milk and her cough was gone after months of dry coughing. So, maybe it is the formula upsetting her tummy, causing reflux and a cough. You can try nursing only and see if that helps (you should try to eliminate dairy from your diet). It may take up to 2 weeks to see a difference (with my daughter it was less than 1 week).