The trick against a dk as melee in a 1v1 situation is that you want to take away all breathing room and kill him as quickly as possible. Here's a little secret about unholy dk's that few people seem to realize:
DKs are not purely a pet, melee or ranged class, but they are all of these simultaneously as well. A good DK will become the role that best suits the situation at hand. Warriors, WW monks and enhance shammies at the moment are better melee classes than an unholy DK when the DK is playing as melee. For example when I am up against a warrior I'll play quite defensively when my cooldowns aren't up. I don't want to engage it in unholy presence because I'll get a beating. I usually go offensive and melee on warriors when I'm able to stun to avoid that parry. The same parry which DKs have. Yes, it is really annoying when you're about to get a kill and you just see "Parry. Parry. Parry. Parry."
Another thing about DKs is that they have very, very little active damage mitigation. There is IBF which is 20% damage reduction for 12s and AMS which is maybe 100 - 150k shield against magic damage. Blood presence and conversion are great for keeping pressure off, but when cooldowns have been blown by opponents I know it's time to kite and avoid, unless my healer is in a very good position.
Lastly, contrary to what people think, DKs don't have much "burst". Their burst has a high ramp up time involving building blood tap stacks, death runes and runic power. A DK could use unholy frenzy, gargoyle, outbreak, festering, festering, empower runic weapon, but it's horribly inefficient and results in less overall damage. A warrior, monk and ESPECIALLY enhance shammy can do much more damage in a shorter period of time.
With the above in mind, when I play against good WW monks that destroy me they simply don't give any breathing room. I get stunned, which I can't not trinket, then fists of fury which I must IBF/desecrate, then I get disarmed which is just 8s of complete failure. I'll asphyxiate which gets trinketted into pet stun which will be all of 1.5s. By the time the disarm ends even with blood presence and conversion I've taken tons of damage. Quick note: Stun and disarm removes parry chance. At that point my only hope in hell is to kite and let my pets and diseases do the work. Problem is that the monk is just not kite-able with flying, rolling and tiger's lust. Also the monk might cast touch of karma which if I use the force I can try to AMS its application. The AMS might hold off on some of the damage, but the problem is not the DoT but rather the damage the monk is NOT taking. If I last until my second asphyxiate is up it doesn't matter because the monk has a second trinket class ability.
There is the whole thing of garg/frenzy coming before or after the touch of karma, but to be honest as an unholy DK I don't know how anyone can force a touch of karma from a monk without having garg up. Unholy just doesn't do enough damage in a short enough period of time.
Anyway, I'm no pro, but the above is my experience with DK.