At it is idomatic, as I suspect you know. The OED defines at it under at as:
16b at it: hard at work, fighting, etc.; busy.
I point this out because I think the etymology of the idiom can be gleaned from the nearest definition of at:
16a: With actions in or with which one is engaged: as at dinner, at work, at play.
In other words, at means to be engaged with, or performing actions related to, a thing. Using this definition, I think the idiom can be constructed with it either being something known from context, or a generic reference (meaning, tautologically, "whatever it is you are currently doing").
So, "while you're at it" can mean "while you are engaged in [something apparent from context]".
I'm going to get a loaf of bread from the store.
While you're at it, get a gallon of milk.
The second sentence meaning, "while you're at (or, "engaged in") the task you mentioned", [do this related thing].
From this somewhat literal sense, we can easily jump to a more figurative sense meaning "to be engaged in that with which one is engaged", i.e., "busy", generically.
To answer your other question, the only other preposition that I know of that might be used in at's place is about. Again, the OED, 11a of about:
Occupied with, attending to; dealing with; interfering or meddling in; attempting...
while one is about it: while one is doing something already undertaken, so as to save time or effort or as a useful addition.