C12: perhaps from Old English tealtrian to waver, and Middle Dutch touteren to stagger
Word Origin and History for tottering
totter
v.
c.1200, "swing to and fro," perhaps from a Scandinavian source (cf. dialectal Norwegian totra "to quiver, shake"). Meaning "stand or walk with shaky, unsteady steps" is from c.1600. Related: Tottered; tottering.