All right, I tend to be a "wait it out" kind of girl, but here is my 2 cents....
My son did the same thing, coughed all night long, and here is what we were told.
When your kids are little, their airways are little. So, while you and I as adults may take 2 weeks to get over a cold, it may take them up to 4 weeks.
HOWEVER, after 6 weeks, I took the baby to the dr and he was diagnosed with allergies. It was as simple as a little bit of Benedryl at night and the cough was gone THAT NIGHT. (I baked cookies for the dr since I was so thrilled to get a solid night's sleep for the first time in 6 weeks!) He only needs it for a few weeks a year, and I swear it makes all the difference during the day when they get a full night's rest!
I would call the dr - at the very least to get the dosage and explain that you think that you want to try it, there is no reason not to. (I think for my guy it was 1/3 of a tsp).
A Tip: Don't get the dye free kind, just plain old benedryl (I even use the store brand), the kids did not like the taste of the dye free stuff.
Don't give her any cough meds - it does nothing for kids this age anyway and recent research suggests that cough medicine doesn't really do anything for coughs for any age.
Good luck!