i believe we covered the DK match up before. but i'll give my input again.
Peach's turnips are everything in this match up. by throwing one, your opponent has to avoid it, catch it, hit it, or reflect it. either way, this creates lag. DK being what i call a "fat character" cannot afford to lag at all. when fat characters lag, they get the worst punishment possible. this is where Peach shines and as long as you keep on DK with Dairs you should be fine (as bad as that sounds.
this is pretty much an auto combo. at the start of each stock chain grab until about early 20s. once DK reaches that point, SHfloat Dair > Dair> Uair (drop float) then, InstaFloat under DK and wait for his reaction. If he Uses his second jump, Chase it! if he air dodges, Land > re-grab (use an Uair to gauge the air dodge if necessary). if your on a stage where a platform is in range, use Dthrow and try to repeat the chasing process. if he lands on a platform low platform, this is good too. Tech chase him with Uair, or Utilt. When Dk gets to a point where he can't be tech chased, air chased or w/e. start glide toss approaching with turnips again. all in all, keep on him at all times. you never want DK to have control of the match.
Refrain from using Fair and Usmash at all costs. at least before DK hits 120% or else you'll probably never kill him. Bair, Fair, Utilt, Usmash, and Bob-Bombs (LOL) will be your best killers.
DK is incredibly heavy and faster than he seems. he has at least 12 different moves that will peach easily and he can edge guard Peach rather effectively. on paper, it doesn't sound like much but Dk's range is really misleading and Bairs are annoying. oh, and
Never tech through Dk, you just Dsmashed. stay in the air (this saves you from.. Earthquake?) stay out of range (this saves you from Bairs). try not to ever attack from the ground. unless you're cornered, then use Dsmash. it's pretty safe and is a sheild piercer.
If this match up is played correctly, the DK user will hate you. Don't forget to stale Dair and Dsmash if you need restore your other moves. overall, i give this match up 55-45 SLIGHTLY in Peach's favor. She can gain control a bit easier than DK can and that's what it comes down to.