Adjoining burial sites to James NAPTHLIA - from the website
Catholic Old Mortuary 1 Section C Row 18 Grave#467
Andrew HALPIN
5 Aug 1883
30 years
Hi Everyone,
My OH followed up on Andrew, any sudden death ought to be subject to an Inquest.
Andrew's inquest was held 18 August, in Sydney with H Shiell presiding. Andrew’s death noted on the index as 7 August. He was aged 30, born United States. He died at Waterloo. The verdict sadly shows he took his own life.

But the admin details also show that there were delays between when the death occurred and when the coroner was able to schedule the formal inquest.

Oh says that I should also mention that the City Coroner was not hearing these cases in a formal court room, but on location.

So for example, a death at PA Hospital, the inquest was noted as held at Camperdown; a death at Sydney Hospital was noted as held Sydney; a death onboard a Schooner was noted as held Sydney; a death at Forest Lodge, inquest held Forest Lodge; a death at Darling Harbour, …. Inquest at Sydney; death Millers Point, inquest Sydney:

So my OH went through the index (almost chronological order ) from June to Oct 1883, none found that could be for Jane.
This suggests to both of us at least, that perhaps she had been attended to by a Medico and that he was able to certify her death without the need for an inquest. The burial register at Rookwood may be the only 'official' record available.
Cheers, JM