Can you take on higher level combat missions in a not-large ship?

I have been mostly exploring for my time in Elite, but recently wanted to get into combat a little bit. I got myself a FDL and decked it out a bit so i could start running some combat missions, but any time I try to do any missions I feel like I do absolutely no damage and my shields last about 10 or so seconds (and I have 4 shield boosters as utility mounts, yes they are all activated and stuff). For example, I took on a threat level 4 combat quest just to test the waters, the target was in a group of 3, so i picked the weakest one to single out first. With a combination of multicannons and beam lasers, I did around 10% to that one enemies shields (attacking the whole time) in the 10 seconds it took for my shields to go completely down. Are these missions just made to be exclusive to the big ships like Corvette , Cutter, and Anaconda, or is there some trick to higher level combat that saves you from just getting melted before you even have a chance to fight? If so, what is the highest threat level mission I should probably take in a FDL until I get one of the large ships? I hope this doesn't sound like a rant because I know its obviously possible I just have no idea how people survive long enough. Thanks!