What I've noticed in the Video is that you stall a bit. After most of your attack you just seem to stand there and do nothing and thats what leaves you open. You need to do a bit of chasing after your opponent and doing some combos on him to do more damage. You need to do this in the air to, try float attacking them. Also you could use the turnips a bit more, they really help.
Another thing you want to do is Dsmash your opponents alot. that helps to build up there damage esspeacially when they crouch cancel.
Here another thing you have to do to improve your game. Float Cancel, and L cancel, but mostly float cancel. You should read this guide.
http://www.smashboards.com/showthread.php?t=41170
And you should also learn to Wavedash It helps with Mind games and makes your opponents vanerable at times.
Oh and one more thing, you've done a good job of sheild grabing your opponent so far.
BTW do you use the C Stick. If not you should.
(oh lvl9 the text above is not for you unless you want to read it. Anyways you seem to be a pretty decent Peach player, just try to improve your game a bit more. And when It comes to Fox ans Falco it's good to spam the Dsmash on them. They have a hard time of escaping it. Esspeacially on a board where you can trap them on a wall. Like onett, or Pokemon stadium, or Corneria.)