The Collaborative International Dictionary of English v.0.48:

Totter \Tot"ter\, v. i. [imp. & p. p. Tottered; p. pr. & vb.
   n. Tottering.] [Probably for older tolter; cf. AS.
   tealtrian to totter, vacillate. Cf.Tilt to incline,
   Toddle, Tottle, Totty.]
   1. To shake so as to threaten a fall; to vacillate; to be
      unsteady; to stagger; as, an old man totters with age. "As
      a bowing wall shall ye be, and as a tottering fence."
      --Ps. lxii. 3.
      [1913 Webster]

   2. To shake; to reel; to lean; to waver.
      [1913 Webster]

            Troy nods from high, and totters to her fall.
                                                  --Dryden.
      [1913 Webster]

WordNet (r) 3.0 (2006):

totter
    v 1: move without being stable, as if threatening to fall; "The
         drunk man tottered over to our table"
    2: walk unsteadily; "small children toddle" [syn: toddle,
       coggle, totter, dodder, paddle, waddle]
    3: move unsteadily, with a rocking motion [syn: teeter,
       seesaw, totter]