Absolutely! What brothers don't experience conflict?
First, no older brother wants a tag-a-long. From early in the story, Doodle's brother tired of bringing Doodle everywhere, so like all young boys he thought of a solution:
Doodle was five years old when I turned 13. I was embarrassed at having a brother of that age who couldn't walk, so I set out to teach him. We were down in Old Woman Swamp. "I'm going to teach you to walk, Doodle," I said.
This is great if it would work for Doodle's brother. It eventually does. This is something brothers do indeed do: set out a purpose and try to fulfill it, even if one of their intentions are not the most positive.
Secondly, brothers will be the most and worst faithful of friends. I think this is strongly displayed in the end when Doodle dies:
The rain came, roaring through the pines. And then, like a bursting Roman candle, a gum tree ahead of us was shattered by a bolt of lightning. When the deafening thunder had died, I heard Doodle cry out, "Brother, Brother, don't leave me! Don't leave me!"
The knowledge that our plans had come to nothing was bitter, and that streak of cruelty within me awakened. I ran as fast as I could, leaving him far behind with a wall of rain dividing us. Soon I could hear his voice no more.
If Doodle's brother hadn't sought his own personal gain in this instance I would have been surprised. I have watched boys. They fight, the ridicule each other and they have a man code, something I will never understand: somehow there can be forgiveness even with the worst of disloyalties. I entirely believe a brother could abandon another if life depended on it.
Lastly, I find that Doodle's brother believed in him when no one else would. This demonstrates a loyalty that is rarely seen in relationships except those between brothers or family members:
Since I had succeeded in teaching Doodle to walk, I began to believe in my own infallibility. I decided to teach him to run, to row, to swim, to climb trees, and to fight. Now he, too, believed in me; so, we set a deadline when Doodle could start school.
Notice, the older brother takes credit for Doodle's successes. Siblings always do this - they want credit for what they do that is good, even if it's just from mom and dad.
This author captures the human nature of a sibling relationship better than most I've seen. It's a completely believable relationship.