I have never seen or heard of that Dark-moon trinket. And personally, I think it looks like a POS. Don't get me wrong, it's a good 378 trinket, but unless it has a very high proc-rate with no internal-CD, it's not going to stand up to a raid drop. T13 Valor trinket is VERY good for DK's too.
So, yeah. Another reason i don't understand why people like askmrrobot. Give me a calculator, Kings, Horn, and a fortune cookie any day over a reforge addon.
As to your spec, you have 3 options:
1) You can keep AM spec (this will depend on you raid make-up of course)
2) You can pick up Lichbourne spec. I think this comes most recommended. Personally, I don't find myself using Lichbourne enough to justify having it, so i dropped it, that will very likely change though when i get my DK into hard-modes.
3) You can load up on DPS talents and be "that guy" who out-dps's half of your LFR group.
The on use mastery is thought to be better because dk's get the shield based on their mastery. So for example if ur in and oh s**t situation u can pop ur trinket, empowered runs weapon ( I hope that's the right spell, one that gives u back all your runes) and death strike twice for a huge shield and a fairly big heal.
On the contrary. I've got it set to Tier 13 Normal up & down. It says my #1 Trinket should be the Soulshifter, as mentioned by Theotherone, and my second trinket should be that Pit Fighter. Also, the Pit fighter is not an on Use ability it's a chance-on-hit.
In fact, here's a screenshot of, what it claims to be, my best-in-slot items.
Chances are I'll end up picking the trinket up anyway, seeing as it's super easy to get. I'll just mess with it and the Valor trinket. I picked up the Valor trinket last night, I'll have to wait for DMF to back around to get this other one.