It's far better to simply wait for the Moon to go away in a week or so. And wait a little longer (July, or August) when it's higher in the sky.
But you do need a scope that can resolve Pluto's low magnitude, a nice dark sky (as in no light pollution), and a really accurate finder chart. An 8" aperture, or larger scope ought to work, when Pluto is near the meridian. you want it to be as far off the horizon as possible.
Visually, you'll want to compare your star chart to your view (even make a crude drawing of what you saw), since Pluto is starlike in appearance. An look at it again at least three nights later, just to confirm that it moved.
I've photographed Pluto over the course of two succeeding weekends, and then "blinked" the images (not unlike what Clyde Trombuagh did, oh so many years ago). This was with my 11" SCT, and an off the shelf Canon DSLR.
I was able to see it move, which was way cool to see happen.