The introduction is probably going to be a bit long winded, I hope it's not too much, but there's a TL;DR at the end.
As some of us might be vaguely aware, and as covered in previous questions (about existence of the sense, history, allowed usages, etc), Indian English currently still makes use of the word "doubt" in the sense of "question", or maybe "concern". In those prior questions, there are some doubts (heh) raised as to the recognition of that sense outside of IndE, and there's obviously no contemporary use in British or American English.
However, an obsolete sense 2 of the noun in the OED seems to be roughly analogous, see e.g. the 17th century usage example:
1693 Col. Rec. Pennsylv. I. 420 You doe Likewise alledge that the greatest bodie of Laws were transmitted‥by Mr. penn, which is a doubt. [OED1]
Another contemporary dictionary, the Century Dictionary, also has a similar sense 2, without indicating obsolescence: "A matter of uncertainty ; an undecided case or proposition ; a ground of hesitation."
Give me leave to tell you, It would seem a kind of affront to our country to make a doubt of what we pretend to be famous for.
Cotton, in Walton's Angler, II. 224. [CENT]
but the Imperial Dictionary (1885) that it's based on only really has sense 4 as in "objection":
To every doubt your answer is the same.
Blackmore. [IMP]
which in Century Dictionary is distinguished as sense 3, so doesn't seem to be the same, and so it seems like it's not a sense lexicographer of the time found essential to document.
Going back further, Johnson's Dictionary (1755) has "2. Question; point unsettled." but I'm not really familiar with 18th century dictionaries, so I'm not sure how to tell if there are any others covering the same sense and if the sense was actually commonly in use back then, or if it was already fairly rare and Johnson simply didn't bother saying so.
TL;DR: Earlier British and American dictionaries do seem to recognise the sense of "doubt" as in "question", but don't really make it clear when it fell out of use.
Given that it has apparently seen use in AmE and BrE, I'm interested in its history in those varieties, and if we can pin down the century at least, if not something more precise, as to when it fell out of use. For example, since the Century Dictionary didn't mark it obsolete, is it that it was used later in AmE than BrE? Was it really still in use in the late 19th century though? What about early in the 20th? For BrE, was there any use in the 18th century? (I don't have an OED3 subscription, so I don't know if it might have later examples. OED2 doesn't seem to.)
Obviously, if it fell out of use later, then it's more likely that the IndE use is simply a conservative form, like many such features in IndE, rather than a reintroduction of the sense, but that part is probably best covered at the other history question. There's probably other interesting questions about the later history of that sense in Am/BrE of course, and some of them might invite comparison. For example, is there any reason why it fell out of favour? In later usage, was it relatively formal? Any usage examples later than the 17th century or so would be great.
References
OED1: James A. H. Murray et al., editors (1897), "Doubt, sb. ¹". sense 2. in A New English Dictionary on Historical Principles (Oxford English Dictionary, First Edition), volume III (D–E), London: Clarendon Press, p. 616, column 2: "A matter or point involved in uncertainty; a doubtful question; a difficulty. Obs." — via archive.org
CENT: William Dwight Whitney and Benjamin Eli Smith, editors (1889–1891), "Doubt¹ (dout), n.". in The Century Dictionary and Cyclopedia, part IV (Deflect–Drool), New York: The Century Co., p. 1745, column 2. — via archive.org
IMP: John Ogilvie and Charles Annandale, editors (1885), "Doubt (dout), n.". in The Imperial Dictionary of the English Language, vol II (Depasture–Kythe), London: Blackie & Son, p. 90, column 3. — via archive.org
Samuel Johnson (1755), "Doubt. n.s.". sense 2. in A Dictionary of the English Language. — via Johnson's Dictionary Online