Define "plasma laden dreadnought".
You should be able to take it out in a mechanical fashion if you have two S plasma torpedos.
Get to range 14, come to a complete stop, and put up 6 ECM. Also put all power in your front shield reinforcement.
Make sure you fire the two S torps at the same shield every time. Watch the bases UI to see which shield you are facing. If you fire as soon as you switch to a new shield, you should hit the next shield. Then go pour yourself a drink and wait for your plasma to rearm. Rinse and repeat. The first dozen or so time will get him to burn a wild weasel shuttle, but after that you'll start slowly accumulating a little shield damage with each volley. Put on some music. Start cooking dinner. You're looking at an hour or more of effort.
Range 14 and 15 are the same for your plasma, but 14 should lure him to fire his phaser 3's. (Thus robbing him of energy for shield reinforcement.) Avoid firing your phasers. Save the power for shields.
You can get a quicker couple of vollys with drones if you can get two waves going in. (2 scatterpacks, or a wave from your bays and scatterpacks.) As soon as he pops the weasel for the first wave, dump out the second wave or scatterpack. The WW will be gone by the time the second wave is ready for impact.
You need to be able to do this at a time when you can follow up, however. If you just wound the sheild and then go back to facing Wild Weasels, the shield will just repair over time and you will have wasted your drones.
-S'Cipio