My dog eats everything, she is outside all day and find objects from allaround including a computer keyboards, handbags, road cones. She has now started gagging and coughing. Would this be from eating foreign objects?

Your dog is out all day? In what kind of weather? Where does she find garbage as you describe, in your backyard ? Do you live in a junkyard?

Sorry, a lot of questions but why do you keep your dog in an environment like that? Of course she could be gagging and coughing from eating god knows what and how old is she?

Dogs can die from bowel obstructions, so my suggestion, is get your dog out of the junkyard and take her to a vet, probably take better care of her, or don't have a dog at all.

This is absolutely a dog lover's forum, maire.
Tick

Wow! You sure do assume a lot! My dog has seasonal allergies that cause him to cough and gag for prolonged periods. My best advice would be to see a vet. Coughing and gagging is often associated with heart problems, allergies, or a "doggie cold". To be sure which one it is, see a vet. I give my dog warm water mixed with a very small amount of cough suppresant (non asprin!) and it helps till we can get to our vet. Good luck!

With a history of eating, chewing, ingesting anything available, the answer points to "yes" it could be from the fact that he has this bad habit.
Any vomiting, diarrhea, how is her appetite? How long has she been doing this?
If it doesn't subside and shortly then you need to get her to the vet.
Of course, it could be other things but if you suspect that this is the problem, you may very well be correct.
You will be very lucky if you don't have to deal with foreign body obstruction in the future, if not dealing with it now.
If it so happens that she is fine this time and not a result of eating something she shouldn't have, you really need to consider a safer environment and lots more supervision.