I hadn't realised that she was noted as being unvaccinated.
You have piqued my interest, I hope you don't mind but I have been doing some background reading. The hospital in which she died only started accepting patients on 31 Jan 1871, before it was fully complete. This was because existing facilities could not cope with all the cases coming with the epidemic, which started in 1868. People were being nursed at home (sometimes unofficially), in huts at other hospitals and isolation precautions that we would recognise today.
The compulsory vaccination Act had been passed in 1853 but this involved people being vaccinated as children. By the time your Jane had died the experts had realised that the vaccine would not last more than 10 years and for working with smallpox then could not be considered to last more than 5 years and by 1871 were starting a programme of revaccinating staff ( possible reason for her being listed as unvaccinated as part of this work). By the epidemic in 1880 staff were then routinely vaccinated every 2 to 3 years and a programme of disinfecting ambulances and compulsory bathing and uniform changing at end of shift were in place for staff. This was not in place in 1871. It wasn't really until 1900 that isolation hospitals were opened away from population centres after research into the 1880 epidemic confirmed growing suspicion that the disease could spread to surrounding populations via airbourne particals etc.
The incubation period is an average of 14 days and up to 17 days and death usually occurs on day 5 to 7 after onset so Jane must have contracted the illness relatively soon after the opening of the hospital.
I found this interesting but I am a geek:
http://www.nhshistory.net/smallpox_and_fever_hospitals.htm