Most MLB records can be found in Records page on the Baseball Almanac
There is no information for rookies and the Cycle.
I don't know if Ryan would be the first rookie ever to do it.
Most RBIs in a game = 12:
Jim Bottomley, St. Louis, 09-16-1924
Mark Whiten, St. Louis, 09-07-1993
Ryan Z needs 7 more to tie it...
An older Rookie of the Year history page (1999) is at:http://www.findarticles.com/p/articles/mi_m0FCI/is_12_59/ai_67045357
The top NL RBI noted was 92 RBIs by Phillies' Scott Rolen in 1997 and
144 by AL's Walt Dropo, Red Sox in 1950.
If you look at the list, Zimmerman is already ahead of many ROY's full year RBI total.