ehm, Gutter, you ever finished the game? (nvm, i saw you got to level 4 so far). cause finishing the game seriously slows down the action and requires you to tackle this like any Rogue Like.. with devious cunning and lots of strategic planning. Well, it's either that or tons of luck.
Auto-picking up stuff would be nice.. if this were a realtime game. However, it is a RL, and to implement this autopickup would either get you killed a lot more (picking up a weapon and unloading it automatically.. but wait, there's an arachnotron there at the edge of my vision.. oh noes now i'm dead) or it would make it too easy (watch me pick up this weapon, unload it and kill that arachnotron all at once!)
edit: on second thought, maybe not such a bad idea after all as long as it can be switched off.
and no, there's no backpack in doomrl.. i think Kornel mentioned somewhere that implementing a bigger inventory would be very hard the way it works now.