That would be considered an "S Trap"
The vent needs to pull off even with the top of the trap arm, not below it.
Move the pipe into the wall and use a tee coming straight out for the p-trap.
i am installing a pedestal sink and the plumbing is coming straight up through the floor...how far down can i install the p trap from the drain
Unless you are in Australia, that type of drain is not permitted. But to answer your question, it depends entirely upon the trap you can find and the room inside the pedestal.