For this particular coding problem, I would use the built-in PriorityQueue or heap functions, rather than rolling your own tree data structure. See http://docs.julialang.org/en/latest/stdlib/collections/ and also the Python example on RosettaCode.
(Basically, my feeling is that on RosettaCode you should try to put together the shortest readable code with reasonable performance, and that means exploiting the Julia standard library where possible.)
