Interesting question. Pole is definitely a noun as it is used in your example. "He" is referring to a fishing pole. The word gather intrigues me. I have not read the book you are speaking about, but I did just discover that gather is a noun. From the Oxford Dictionary: Gather Noun( gathers) a part of a garment that is gathered or drawn in.
To gather in the woods, means to pick up some food in the woods. If you keep reading you will see they have collected a bag of greens, and a gallon of strawberries.
Yes, if you read on, you'll find that they collected strawberries, greens, and fish.
So I presume that they went gathering first and then they went fishing.
But it is completely illogical. Why would somebody say let's go fishing, and first thing after that let's leave our fishing poles in the woods and go gathering instead?
There's no 'instead' in all of this - they do both.
This conversation takes place between 2 people who are the best of friends, and know each other very well. You need to take that in to account, when reading this conversation (and many to come), between Katniss and Gale - that they don't use many words, because they know what the other part means, without a lot words.