Have you contacted the Queen Victoria Museum in Launceston? The museum in Inveresk is located in the old railway workshops and they may hold records relating to the railway station.
I checked the records I have for the CofE burial ground Aka Cypress St. but no Annie Howard and the General Cemetery Charles St. no luck. Some of the burial records haven't survived, and the records I have consulted were compiled from headstones inscriptions and a card index which records details of burials at Cypress St. if they were CofE you could check the church burial registers.
If you know her religion that would help identify the likely cemetery. Unfortunately most of the early cemeteries in Launceston no longer exist.
regards Lee-Ann