As a D3 main, I have to disagree with you, Nicole. I think D3 wins this MU at LEAST 55-45. Either way (not a fan of the numbers), D3 has the advantage. Both D3 and Peach have very distinct strengths.
Peach can rack damage, apply great shield pressure, and has a very frustrating projectile that helps her zone very well.
D3 has the offstage advantage, bair, grab range+chaingrab, great kill power, and an incredible knack for living to 180+ many lives.
However, this match-up for Peach is ALL about spacing on D3's shield and beig patient when getting inside D3s zone. As Nicole said, NEVER land near to/in front of the D3. I rarely get grabs on Nicole, who I play a lot. She will float, dair my shield for pressure, and either perfectly space a fair on my shield or fall nair to shieldpoke, with other mix ups. The point is, it's almost his and run. Get in, give the damage you can, then play safe and respace, rinse and repeat.
Some things that can help in this MU:
-don't be predictable with your floats. Peach has a strong ground game too; use that to your advantage, keep the D3 on his toes. Otherwise, you'll hit bair city.
-use turnips, ALWAYS. they mess with D3, in my opinion, a lot
-JAB; seriously, this is a great move, and is a great set up. it's a great move to use if you feel in trouble or pressures
-to reiterate: NEVER LAND BY D3
-recover high if possible; don't get caught below the plain of the stage when D3 has the edge etc
usmash goes through D3's landing upb
-many D3s dont CG Peach right; you have to buffered runnin shield grab her...if they don't do that, or they mess up, jab goes beats it (many of you know this I assume), so your best option when getting Cged is the spam jab, not spot dodge or some dumb **** like that
-if you are at high damage, try to AVOID approaching with a head-level float; uptilt will beat you. also, if you are predictable with float, it's possibly for D3 to simply roll behind you right when he expects you to float and uptilt...as I said, DONT BE PREDICTABLE WITH YOUR FLOATS!
-overtilt. it's a great move.
This is a MU I know pretty well, I think. I'm really confident against Peaches. In the end, I feel its in D3's favor overall, more so if the players are unfamiliar with each other. If the players play a lot, I feel it's more evenish and the better player will win relatively consistantly.
Good luck, hope this helped a bit!