Are godt and bra interchangeable?
Wouldn't "Jeg har det ganske bra, takk" working as well?
Yes, if the question was about how you are, both answers would be equally acceptable.
But the DL answer could also be given in response to someone asking, say, how is your homework coming along, or how is a work project going?
Would "veldig" be acceptable here instead of "ganske?" I would have thought "ganske" would be more appropriate had the sentence read "It is going pretty well, thanks."