It's been a while since I've played, but the Doom is one of my favourite vanilla ships. You're right that it's slow, which is why you absolutely need to put Augmented Engines on it. That's also what it's ship system is for; you flare out their engines, then phase and fly through them while turning. Loadout is also very important. You want overwhelming burst firepower, and enough capacity to take advantage of that. For phase ships in general, I've found, you want capacitors a lot more than you want vents. Your phase speed gives you the mobility to run away far enough to active vent safely, so you want to have enough capacity to run absurdly overpowered loadouts and not instantly overload yourself. On the Doom I run 4 AM Blasters, 2 Heavy Blasters, 2 Typhoon Reaper Launchers, and 4 Burst PD. Very heavy on the flux and needs heavy investment in capacitors and +OP skills just to be able to mount and fire all that weaponry without overloading when it tries to cloak, but it is worth it. Pick a cruiser or capital, cripple it with the ship system, get behind it, and give it all 4 AM Blasters at once. If it's overloaded or without rear shield coverage, and unless it's a Paragon or an Aurora it is, then give it two Typhoons as well. Cloak before you overload yourself, retreat, vent, repeat. Killing destroyers is much the same, except you don't have to get behind them or use Typhoons. 4 AM Blaster shots will instantly overload anything but a Medusa, and the Medusa will be sent over the edge by the HBs. The HBs rip apart destroyers pretty quickly, so you don't need to spend Typhoons on them if you don't want to. Frigates, don't even bother with the AM shots. Just cripple and let your HBs rip them apart.
The Doom does have weaknesses, though. You handle pretty much anything 1v1, but the Doom doesn't fare particularly well when fighting multiple opponents because, being a phase ship, it has no shields. It can easily overload a single ship and lock down their weaponry through sheer damage or just use the phase speed to get behind them, but that won't do anything about the Enforcer on its flank with a Heavy Mauler. If the Doom is to solo any greater number of ships, it needs to pick off stragglers or overextenders and carefully limit the amount of fire it gets exposed to; it has a lot of armor, but armor doesn't grow back. It shines in fleet actions, where it has support and distractions, not as a solo flagship. That's not to say that someone can't use it as a solo flagship, but that there are other ships far better suited for the role.