Sadly you'll find she's not so good against actual people
And therein lies the problem, mr-bagpipes. Hard AI will not quite get you ready for online action against decent players, but at least you'll have a feel for Queen's abilities. Anyhow, as others have said already, invest in (and use) spikes early and often, along with Brambling Shield. She's a killer on enemy armor and can be decent against structures. I personally don't invest in Shamblers, or at least not before maxing out these other three abilities (ground spikes, spike wave, & shield). The only minions that you should really be concerned about are idols, which you should get as soon as possible (starting with a healer). You probably already know that Queen's abilities (and much of her battlefield usefulness) peak at about level 10 versus other demigods; after that, it doesn't much matter what you invest your level-up points in.
Regarding items, I highly recommend the Cape of Plentiful Mana as the optimal favor item. Combined with a Vlemish Faceguard (or even the Plenor Battlecrown), your mana needs should be mostly taken care of for the whole game. Depending on the map, the Amulet of Teleportation or the Swift Anklet is also a viable option for Queen. Also, the Staff of the Warmage is a solid early-game favor item, but I think that the Cape of Plentiful Mana is better for the long haul. I think that the ideal inventory will have one or two good mana items (I like Vlemish and Plenor as soon as can be afforded), one or two health/armor items (such as Hauberk of Life, Nimoth Chest Armor, or Unbreakable boots), and 1-2 items tailored to the occasion, which might include Boots of Speed, Gauntlets of Brutality, etc. I don't believe in a single one-size-fits-all build for every game, so I would advise experimenting with various inventories.
In looking at your build, I have to admit that there is something to be said about stacking health and armor on QoT. I rarely do such a thing since she is so mana-dependent (and needs good mana items first), but you can really surprise opponents by getting enough health and armor to stand toe-to-toe with them, especially when they expect for you to run at the first whiff of damage. With a Brambling Shield up, you can really freak out an opponent by simply standing your ground for a moment (if your health will allow it). Actually, with competent usage of spikes and Brambling Shield, Queen is one of the better demigods at psyching out and kiting (cat-and-mouse action) opponents. It's just a pity that her minion build is not stronger and most of the time she will, indeed, have lower health than other demigods.
Have fun and good luck to you!
P.S. One thing I've noticed in playing QoT online is that a lot of other players don't really know how to relate to her. Sometimes, even your allies will be baffled, largely because she is played so infrequently. In my experience, some human allies believe that she's a waste of time; others believe that she should be their demigod's personal minion and shield-provider the entire game; and yet others believe that she should be on the front lines racking up kills like UB, LE, and Oak. Anyhow, try not to be discouraged by any of this. She's a fun character to play (though she needs a slight buff), so just try to figure out a playstyle that fits you and will help your team. Admittedly, she teams up better with some demigods (such as the heavy hitters) than others, and I think that she can rival Sedna as a support demigod in some situations (though I wouldn't suggest playing her as merely support or as somebody's minion). Above all, have fun with her--we need more good QoT players out there!