Yes, while the etimology (separating the compound word) of μονογενής is only begotten, the word actually means unique, one of a kind.
μονογενής (monogenēs), ές (es): adj.; ≡ Str 3439; TDNT 4.737—LN 58.52 unique, only, one and only, i.e., one of a kind: (many versions) only begotten (Lk 7:12; 8:42; 9:38; Jn 1:14, 18; 3:16, 18; Heb 11:17; 1Jn 4:9+; Jn 1:34 v.r.) -- Dictionary of Biblical Languages with Semantic Domains: Greek (New Testament)
Here is Bruce Metzger's comments from A Textual Commentary on the Greek New Testament, Second Edition
1:18 μονογενὴς θεός {B}
With the acquisition of 𝔓66 and 𝔓75, both of which read θεός, the external support of this reading has been notably strengthened. A majority of the Committee regarded the reading μονογενὴς υἱός, which undoubtedly is easier than μονογενὴς θεός, to be the result of scribal assimilation to Jn 3:16, 18; 1 Jn 4:9. The anarthrous use of θεός (cf. 1:1) appears to be more primitive. There is no reason why the article should have been deleted, and when υἱός supplanted θεός it would certainly have been added. The shortest reading, ὁ μονογενής, while attractive because of internal considerations, is too poorly attested for acceptance as the text. Some modern commentators4 take μονογενής as a noun and punctuate so as to have three distinct designations of him who makes God known (μονογενής, θεός, ὁ ὢν εἰς τὸν κόλπον τοῦ πατρὸς …).
[It is doubtful that the author would have written μονογενὴς θεός, which may be a primitive, transcriptional error in the Alexandrian tradition (Υς/Θς). At least a {D} decision would be preferable. A.W.]