Generating random permutations is quite a different problem from creating random numbers. The standard algo for random permutations is the Fisher-Yates Shuffle.
ETA: As you don't want to store the permutation, you might want to pick a number randomly from 1 to n!, and then generate the permutation on the fly up to the desired element, using the techniques outlined here:
If one really wants to do it the slow and hard way, it's possible to compute a random permutation of n elements one element at a time with n bits of storage (less with fairly generic compression techniques): just remember the set of numbers that have been produced so far and sequentially pick one of the remaining ones.
You'll waste some combination of additional memory (for arithmetic decoding state) and random bits (for rejected samples), but materializing a large randomly permuted vector should be slower.