Transforming the sorting problem into Dijkstra
What you want is to reduce sorting (or element uniqueness) to the single source shortest path problem (rather than to Dijkstra's particular algorithm!) using an $o(n\log n)$ time reduction whose output has size $O(n)$. Then you will get a tight decision tree lower bound in the algebraic decision tree model for constant degree (Dijkstra's algorithm can be implemented using a linear algebraic decision tree).

Such a reduction is probably not known. See for example D.W.'s question on cstheory.