Quickbeam is a solid hero for solo thanks to his readying, but he does pose some deckbuilding challenges. He is a 12 threat hero, which already restricts the other heroes you can choose. On top of that, his ability pretty much requires you to include Lore for healing (again, thinking in terms of solo). Perhaps the most stable solo build is Quickbeam, Elrond (for that double healing), and a Lore Hobbit (for low threat). I wanted to do something a bit different, and this is the result!
First, I decided to include Bifur as my sole Lore hero and run two Tactics heroes instead. The benefit of Bifur is that he is low threat and his ability allows you to essentially operate as if you have two Lore heroes, while having the flexibility to pick a hero of a different sphere if you want. In this case, I've opted for Tactics Théoden as my third hero for one main reason: extra willpower. I struggled with willpower in some of my other pre-Théoden versions of this build, and I realized by including him, I could greatly increase my available willpower at the beginning of a game, which is the most crucial part. In the mid and late game, I generally have enough willpower, but it's at the start that I need the extra help that Théoden provides, and it's nice to get extra value out of Quickbeam's readying by turning him into a 3 willpower quester. He also is versatile in terms of attacking and defense, which I've supplemented with Captain of Gondor and Raiment of War.
The surprising thing here is that while Elrond's healing is super useful, this deck does well in the healing department without him. Between Warden of Healing and Wellinghall Preserver, Quickbeam does fine in terms of being able to use his ability. It also helps that once the Ent army gets going, Quickbeam doesn't need to do much readying. So, similarly to Théoden's role, Quickbeam's readying is really vital for the early game, whereas the ally Ent army takes over in the mid to late game.
One final thing is to understand about this deck is that it can get caught with its pants down by early enemy attacks, especially if you have to quest hard. I retooled the deck a bit to counter this so that there are now 4 separate ways (12 cards worth) to handle defense in the first round. You can put out a Defender of Rammas, use Feint to cancel attack, use Hold Your Ground! to ready Théoden so he can defend, or put Ent Draught on a character and have them take an undefended attack. With these many options, you should draw at least one of them in your opening hand. Speaking of the opening hand, Treebeard is the main card you want to see (apart from the defensive options I just mentioned), as once he is on the board, then the deck can really start humming along.
I've had mixed success with this one against more difficult quests, especially ones that require a fast pace (Race Across Harad is a good example). If you are taking on a quest that gives you some control of the pace, though, then this deck will probably roll right over it. Enjoy!