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Yes, this is a bug. Typing Q.multiplicity?? we see that it calls X.multiplicity(Q) and X.multiplicity?? shows that it changes the monomial ordering to negdegrevlex and then tries to use the interface to Singular. However the interface to Singular is broken for univariate polynomial rings with "local" monomial ordering (it always uses the global ordering instead); I reported this as trac ticket #27479.
As a temporary workaround I guess you can add a variable and set it to zero:
sage: A2.<x,y> = AffineSpace(QQ,2)
sage: X = A2.subscheme([x^1789+x,y])
sage: Q = X([0,0])
sage: Q.multiplicity()
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