From reading your summary, I know the inspiration and purpose of this piece, and of course the identity of the "young man" mentioned in the first stanza. I'd like to say I'd've known without having such a summary, but I'm not sure that's true -- although I'm quite familiar with the book, it would take me on a sharp day to pick that reference out. That's not a critique -- I think you alluded to it well, although you might question for yourself whether you want to invoke it to a greater extent, and perhaps consider threading other nods through the rest of the poem to strengthen the tie to the source of inspiration.
I love the last stanza. My first thought upon reading it was "Wow. This poem made me think a great deal more than I thought it would." That turnaround from a rather simple query to a more profound philosophical quandary is a good one -- and also turns back on the assumptions made about the narrator of the poem asking such a seemingly simple question. In that way, the opening and the closing book-end the poem quite nicely.
The piece might gain impact if you gave your little duckling a gender, especially since everything else in the poem is gendered (up to and including that little duckling's "brothers"). It would automatically make him (or her!) more relatable, more sympathetic. Is it important that we sympathize/empathize with the little duckling? That's a question for you to decide, but in my view given the turn of the last stanza it's important for the reader to feel some sense of relation there. It actually adds a lot more than I even suspected it would. Wonderful work.
Overall, an enjoyable read. I always appreciate a good narrative poem and you've pulled this one off well.