Have you already done the Annuminas quests? I think that area is ~level 40 now, and is the highest level landscape in Evendim. You might be able to get a level or two there, a nice bit of quests.
After that though, the zones for mid 40's are Forochel, Angmar, and Misty Mountains. You only need one of the three, but each person has their preferences so I can't say which you'd like the best. (My personal favorite is Misty, since there's a level ~46 quest that lets you explode a goblin camp.) I think there's some low to mid 40's quests in Trollshaws - Echad Candellath also if you already have that region unlocked, but not enough quests there to get you very far.
Once you get to ~46 you can start the volume 2 epic, which you need to do some of before you can enter Moria. (I think it starts in Rivendell.) The quests for that epic are level 50, so it's a question of how comfortable you are underlevelling quests as to when you start. After going far enough in the epic, you will get a starter legendary item (LI) that you need to get to level 10 before you can advance. In other words, head back to whichever mid-40's zone you unlocked to quest and kill things until your LI levels enough, after which you can start Moria.
Gremblus, Seuer, Grelob, and various others of Arkenstone