Gotta mix it up more... you approach with nair WAY WAY too much. You pill too close and often have issues with the stages. Gotta watch out for gimp kills. As Doc, don't waste your double jump near the edge.
Waveland. Use bair *tons* more. It is a great tool to apply pressure. :D I liked how you got up from the ledge with Nair, but that peach could have just backed up and dsmashed/grabbed you every time. Mix it up, try edgedashing. Keep moving. Wavedash more to do so. If you get close and she is just shielding or the like, apply pressure with bair.
The peach was definitely controlling all of the matches. Realize that you don't need to nessisarily rush in (bleh its horrible against peach) but rather you can will learn to move around and then see a good window to start stuff up. When you do get a grab, consider something besides Bthrow, and you should have followed that up with bairs.
Don't CC the downsmash, but I bet you know that. Try to force things like rolls. If you don't let them control the match you can definitely start getting moves like the dsmash in (even though it is risky in this matchup). When you do go in with bairs or fairs, don't space it so she can still grab you. You can hit her shield and be outside of her grab range. gotta learn the spacing well for this match.
Keep up the practice.