A good leveling guild can be a great resource. In your shoes, I would look to join a larger guild that advertises as a leveling guild....there should be people around your own level to do dungeon runs with, and guildies are almost always much much nicer to each other, more understanding of beginners. If you're planning on getting to end game and doing any kind of raiding (even LFR), the dungeon practice will be good. In a leveling guild you should find people happy to answer questions. Dungeons will drop better gear too.
Also, and I mean no offense but only to be helpful....if 2 of you are going into a zone even slightly above you and being regularly overwhelmed, there are some things you're simply doing wrong. Without watching over your shoulder I can't tell you exactly what, but I'm thinking your pulls are too big. Caves in particular can overwhelm you; out in the open you can see better, and pick areas with scattered mobs rather than clumps. Beyond that, if you haven't yet try reading a bit in the class forums for advice, although those are almost invariably written for end game. Studying your spell book closely might yield some new understanding of the spells and how they interact....to this day, I reread my spell book every few months. If you can figure out what types of things you're doing wrong, it's totally easy to fix those problems.
And, both of you should be dps, you can throw the occasional heal on each other (off-healing) but when the mobs die faster, you don't (duh!) Questing is actually designed to be done solo, so with 2 of you, going into higher areas (slightly) should be doable.
Lastly, although AH prices tend to be high, it never hurts to check there for a couple gear upgrades. More than once I've seen something over priced (for transmog) and sent a mail to the seller offering a much lower price (for leveling gear) and had my offer accepted.
If you post about specific instances of being overwhelmed: location, quest name, how you approached it, what kind of problems you had......people on this forum will give more exact suggestions. I know you say you want to speed up the leveling process, but I recommend focusing on correcting the issues that are making the process difficult. Then you'll start having more fun, whether it goes quickly or not.