You might try (as a temporary measure) putting a vinyl runner guard or a thick plastic drop cloth over the new rug. Cats usuall hate getting wet feet from their pee and if she goes when you aren't looking she won't like what happens and at least the rug will be protected....

Hopefully she will stop now she knows she isn't supposed to go there. (If the rug contains wool or flax that has been naturally dyed, it is possible she is smelling the urea that is used in some dying processes and is reacting to that.)