In “I wonder the origin of the word”, origin appears to be the direct object of the verb, with wonder being used transitively.
OED has examples of this use, which is equivalent to the modern wonder at:
†3. a. trans. To regard with wonder; to marvel at: often implying profound admiration (cf. wonder n. 7c). Obs.
1593 B. Barnes Parthenophil & Parthenophe 18 : If she be silent euery man in place With silence wonders her.
1821 C. Lamb My First Play in Elia 1st Ser., : I knew nothing, understood nothing, discriminated nothing. I felt all, loved all, wondered all.
However the modern wonder about does not appear to have its equivalent in an obsolete transitive form:
†3. a. trans. To regard with wonder; to marvel at: often implying profound admiration (cf. wonder n. 7c). Obs.
3. b. impers. pass. it is to be wondered = it is to be wondered at (1d). Now rare or Obs.
†4. To affect or strike with wonder; to cause to marvel, amaze, astound. (See also 1f) Obs.
Even defintion 1b is listed as intransitive:
1. b. with clause expressing the motive or object of wonder.
1846 W. Greener Sci. Gunnery (new ed.) 133 : We wonder the parties did not take a patent for the discovery.
This is quite close to the original form, but again is wonder at, not wonder about. The meaning wonder about is listed as “usually with clause” rather than transitive with an object:
2. Usually with clause: To ask oneself in wonderment; to feel some doubt or curiosity (how, whether, why, etc.); to be desirous to know or learn.
a1616 Shakespeare Winter's Tale (1623) iii. iii. 69 What haue we heere? Mercy on's, a Barne?... A boy, or a Childe I wonder?
That citation appears to use a child as the grammatical object of wonder in the meaning wonder about. But the definition is still intransitive.
OED does have a note
I wonder is often placed after a question which expresses the object of curiosity or doubt; e.g. ‘How can that be, I wonder?’ = I wonder how that can be. Also I wonder!, colloq. exclamation expressing doubt, incredulity, or reserve of judgement.
So it appears that wonder can take an object (albeit in an obsolete use) if the meaning is wonder at but not if the meaning is wonder about.