WordNet (r) 3.0 (2006):

get going
    v 1: begin or set in motion; "I start at eight in the morning";
         "Ready, set, go!" [syn: start, go, get going] [ant:
         halt, stop]
    2: start to be active; "Get cracking, please!" [syn: get
       cracking, bestir oneself, get going, get moving, get
       weaving, get started, get rolling]

Moby Thesaurus II by Grady Ward, 1.0:

86 Moby Thesaurus words for "get going":
   attack, be off, beat it, begone, break in, bundle, bustle, chase,
   clear out, crowd, dash, dash off, dash on, dive into, double-time,
   enter on, enter upon, fall to, festinate, flake off, get, get busy,
   get cracking, get in there, get lost, get moving, get off, get out,
   get squared away, get under way, get with it, git, go to it,
   hasten, hit the road, hop to it, hurry, hurry on, hurry through,
   hurry up, hurry-scurry, hustle, jump to it, launch into, leap,
   light into, lose no time, make a beginning, make a move,
   make haste, make yourself scarce, move quickly, pitch in,
   pitch into, plunge, plunge into, post, press on, push on, race,
   run, rush, rush through, sail into, scamper, scram, scramble,
   scurry, scuttle, set a course, set about, set at, set to,
   set to work, shove off, spurt, start in, start up, tackle, take on,
   tear, turn to, undertake, vamoose, wade into, warm up