You could always just use Data.Sequence.
Alternatively, a well-known implementation of a purely functional queue is to use two lists. One for enqueue and another for dequeue. Enqueue would simply cons with the enqueue list. Dequeue takes the head of the dequeue list. When the dequeue list is shorter than the enqueue list, refill it by reversing the enqueue list. See Chris Okasaki’s Purely Functional Datastructures.
Even though this implementation uses reverse, the amortized time cost of this is insignificant asymptotically. It works out so that for every enqueue, you incur a time debt of Θ(1) for the dequeue list refill. The expected time of a dequeue is therefore at most twice that of an enqueue. This is a constant factor, so the worst-case cost of both operations is O(1).