Hello. My ship, despite what my combat level my suggest, is fairly weak. At level 25, I can barely survive. I think that my damage cap is 82. The only reason that I'm surviving/killing is because of traps and 5 hardened duratinum hulls. I have only researched weapons until heavy plasma, working on that though. I have 3 low research cores, so i have 161 energy. Am I simply ranking to fast for my level?

I would say it depends on a couple of things :
1. what race
2. what profession
3. what is your RP / hour -> only planet production that matters at your level honestly
4. if you are in a legion ( most likely since your on the forums ) what is the base geared towards RP, or arti? ( if the answer is mining, then RUN, run very very fast!!! )

something you could try is adding a sensor to find some softer targets, those that want to be left alone at your level do so really easily by adding 1 or 2 small cloaks.

Konqul Fixer. My legion is Rp is 84. I kind of wanted to make my own. My RP per hour is 159. I have a sufficient amount of Cr, so modules on my ship won't be a problem, here are my modules @rank 25, 5 reinforced duratium,dominion cannon, 2 heavy plasma cannons, 2 offline plasma cannons, and 4 energy modules: 3 graviton cores mark 2 and an omicron injector.

84... Points per ship? If so, it'd help to get into a legion with a higher level base, that splits shipments evenly (there are plenty of level 4s and 5s giving 10,000 to 25,000 points per ship). Best not to make your own legion at that rank, as you probably have neither the energy nor the resources to make it pay out at a sufficient level.

EDIT: Lol I can't read. Anyway, keep killing as you have been, and get another dom cannon. It should help a bit.