This is why I dislike these "simulator" they are never accurate. The TITAN is not quite a science ship with the outfitting of Quantum torpedos.
The type of ship doesn't really matter, it's what tier they are in. Tiers are based on what rank you are, the higher the tier the more choice you have in selecting what torpedo or beam weapon types you can outfit her with, the Luna-class is a higher tier ship.
Science will only really determine how many stations you can have on your bridge, science ships obviously have more science stations, tactical ships have more tactical stations and so on. It will also limit how many weapons you can put on your ship, though not the type of weapon.
For example, let's say you had eight weapon slots: You could put four phasers and four torpedo launchers on her, or you could put two phasers and six torpedo launchers, maybe you'd like six phasers and two torpedo launchers instead. You get the idea.
However since the game takes place in the year 2409 Quantum Torpedoes aren't exactly going to be the best torpedo type anymore.