The Collaborative International Dictionary of English v.0.48:

doddering \doddering\ adj.
   1. shaking as from old age.

   Syn: doddery, shaking, tottering, tottery.
        [WordNet 1.5]

   2. mentally or physically infirm with age.

   Syn: gaga, senile.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

doddering
    adj 1: mentally or physically infirm with age; "his mother was
           doddering and frail" [syn: doddering, doddery,
           gaga, senile]

Moby Thesaurus II by Grady Ward, 1.0:

59 Moby Thesaurus words for "doddering":
   aged, anile, childish, childlike, crabbed, debilitated, decrepit,
   dilapidated, doddered, doddery, doited, doting, faltering, feeble,
   fossilized, frail, gerontal, gerontic, groggy, infirm, mossbacked,
   moth-eaten, mummylike, old, palsied, papery-skinned, quaking,
   quavering, quivering, ramshackle, ravaged with age, reeling,
   ricketish, rickety, rocky, run to seed, rusty, senile, shaking,
   shaky, shriveled, spidery, spindly, staggering, stricken in years,
   superannuated, teetering, teetery, timeworn, tottering, tottery,
   trembling, trembly, tumbledown, unsteady, weak, withered, wizened,
   wobbly