Are you looking at the actual form or at a transcription of the form? ... the long-hand script can be very much just a scribble at times, and in my view IRWIN and IRVINE can be mis-read either way. The NSW BDM online index has the marriage as IRVINE, but I know that it was not until the 1930s that any index by surnames was available for NSW BDM staff. The current index was originally prepared by volunteers working under natural light and coping with the fragile records back to 1787, bound up into volumes by around 1912, and subject to much thumbing through, ink bleeds, torn corners, missing pages etc since their original preparations.
If your 1848 document says she arrived free on the Adam Lodge, then I think that if it is the Permission to Marry, that would be reliable.
I can see John and Rebecca were married at "NL" - That would be St Andrews, Church of England,
https://www.bdm.nsw.gov.au/Documents/early-church-codes.pdf I can see the birth and baptism for Sarah Rebecca

daughter of John and Rebecca SIMS, born 4 February 1849 and baptised 4 March 1849, See NSW BDM baptism record for 1849, volume 34A, line 28. John SIMS was a stonemason. The baptism ceremony is recorded in St Philip’s C of E, Sydney by Rev William COWPER.
I will try to check further, but it may be some days before I have spare moments to get to my own offline resources for that decade after the ceasation of convicts to NSW and before the gold rushes ...
ADD
https://www.bdm.nsw.gov.au/Pages/about-us/history-of-registry.aspxJM