Royal baby: Duchess of Cambridge goes into labour
The first reference I can find that is a reliable use of 'labour' in regard to childbirth is in the King James (Authorised) Bible of 1611:
And they iourneyed from Bethel: and there was but a litle way to come to Ephrath; and Rachel traueiled, and she had hard labour.
The OED has a few quotes before that (see below) but they do not seem as clear to me (in relation to childbirth).
However, in 1623 Shakespeare, no doubt influenced by the KJV, uses the noun in relation to childbirth:
Shakespeare & J. Fletcher Henry VIII v. i. 18 The Queens in Labor They say in great Extremity, and fear'd Shee'l with the Labour, end.
And there is a metaphoric use of the noun in 1634:
T. Heywood Maidenhead Lost i. B 3 b My brain's in labour, and must be deliuered Of some new mischeife.
So was it the KJV bible which first used the word 'labour' as a noun in relation to childbirth?
OED references earlier than 1611:
1472 J. Paston in Paston Lett. & Papers (2004) I. 452 God spede yow, and Owre Ladye hyre to hyre plesure, wyth as easye labore to overkom that she is abowt as euyre had any lady or [gentyll]-woman saff Owre Lady heer-selffe. And soo I hope she shall to hyre greet joye and all owres.
?1529 R. Hyrde tr. J. L. Vives Instr. Christen Woman sig. Kivv Wherfore she was worthy to beare a chylde with great payne and werynes: and in her labour to be delyuered of her chyde [sic] and her lyfe both.
1580 T. Newton Approoued Med. f. 84 v In the tyme of the byrthe & labour bounde to the Leage, it bryngeth forthe the chylde wythout payne.
1595 Spenser Epithalamion in Amoretti & Epithalamion xxi. sig. H6 Sith of wemens labours thou hast charge, And generation goodly dost enlarge.