I can trace some useful background for 41 Hamilton Street, West Hobart, but the publicly indexed material does not yet give me a reliable construction date or a chain of ownership for number 41 itself.
What I can establish is:
Hamilton Street was originally Adelaide Street. Libraries Tasmania records the change from Adelaide Street to Hamilton Street at about 1897, apparently to avoid confusion with Adelaide Street in South Hobart.
The street itself is considerably older. Adelaide Street was laid out as part of the expansion of Hobart’s northern suburbs in the 1830s. By 1841, however, there were still relatively few houses beyond the main streets in this part of West Hobart.
Hamilton Street subsequently developed as a residential street, with substantial building activity in the late 19th and early 20th centuries. The City of Hobart’s heritage material identifies several surviving historic houses in Hamilton Street, including 9, 17, 30, 53, 62 and 64 Hamilton Street. Interestingly, 41 Hamilton Street is not individually listed as a heritage place in that inventory.
The City of Hobart’s historical material says that nine houses were built by the Council in the Hamilton Street area in 1930, as part of its attempt to provide subsidised housing during the Depression. Whether 41 Hamilton Street was one of those nine requires checking the original council records and plans.
Today, 41 Hamilton Street is recorded as a four-bedroom, two-bathroom house on about 604 m², with approximately 178 m² of building area. Current property databases don’t provide a historical sales record for the address.
The location of 41 Hamilton Street puts it in an area where the character of the housing changed substantially during the early 20th century. The City’s heritage studies describe groups of inter-war residences in this part of Hamilton Street, and specifically note the homogeneous scale and character of dwellings around Hamilton Street.
So, rather than relying on the modern real-estate databases, the best way to establish the history of 41 Hamilton Street specifically would be to work backwards through:
Hobart City Council rate books – these can identify the owner and occupier year by year and sometimes describe the building.
Libraries Tasmania’s LIST/title records – to establish the original parcel and successive owners.
Hobart valuation/rate assessment records – particularly useful for determining when a house first appeared on the property.
Historic maps and plans – especially the 19th-century Hobart plans and later sewerage/municipal plans.
Trove newspapers – searches for "41 Hamilton Street" and, importantly, the previous address “41 Adelaide Street”, since the street was renamed around 1897.
I would particularly like to investigate the Adelaide Street records, because that could reveal whether the present house existed before 1897 or whether the current building replaced an earlier dwelling.
If you’d like, I can  dig much deeper into 41 Hamilton Street and try to establish its original owner, date of, occupants and any interesting events associated with the house, using old maps, rate books, Trove and Libraries Tasmania records.
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Yes. I have now gone back to the question of reconstructing the actual property history, rather than relying on modern real-estate sites.
There is one important correction to my earlier answer: I cannot yet substantiate that 41 Hamilton Street was formerly numbered 41 Adelaide Street. What we can establish is that Adelaide Street in West Hobart was renamed Hamilton Street in 1897, so an address in that part of the street before 1897 would have been recorded as Adelaide Street.
The most promising primary-source trail is the Tasmanian Archives census and land records. A genealogical researcher has specifically identified the Archives census series CEN1/1/23–139 as covering Adelaide Street, described as the street now called Hamilton Street, running between Hill Street and Butterworth Street. This demonstrates that residents were being recorded in Adelaide Street in the 1840s.
However, that does not prove that the present house at No. 41 stood there in the 1840s. The land could have been vacant, occupied by another house, or subsequently subdivided.
There is also an intriguing piece of local history: the area around Hamilton Street contained a burial ground operating from 1840 to 1872, and surviving local historical research suggests that some of the original burial ground may have extended beneath later residential properties.
Modern property databases are of little help. Domain specifically reports no recorded property history for 41 Hamilton Street.
That means the answer is unlikely to come from real-estate websites. We need to identify the original land parcel and then follow it through the Tasmanian titles.
I would therefore reconstruct it in this order:
1. Historic survey/plan
Locate the block corresponding to today’s 41 Hamilton Street on an early Hobart plan.
2. Original land grant
Determine whether the land was part of an early Crown grant or a later subdivision.
3. 1840s–1890s rate/census records
Identify the occupants of the relevant parcel while it was still Adelaide Street.
4. 1897 street-name change
Match the old Adelaide Street property to the subsequent Hamilton Street address. The name change itself is firmly documented.
5. Building evidence
Look for the first appearance of a house in rate books, building applications, valuation records and newspapers.
6. Title succession
Trace owners through deeds and title records.
The historical evidence suggests that Hamilton Street’s development was not simply a twentieth-century development. Adelaide Street was already occupied in the 1840s, and the street-name change occurred in 1897.
So there are now three plausible possibilities for No. 41:
an existing nineteenth-century house which survived and was renumbered;
an older house which was demolished and replaced around the Federation period; or
a later house built on a subdivision of an older property.
At this stage I would not assign a construction date to the present house.
I can go further and try to identify the actual allotment containing 41 Hamilton Street on historic maps, then work outward to its neighbours—39, 40, 42 and 43 Hamilton Street. That is likely to expose the original subdivision pattern and, from there, the name of the original owner.
The fact that 43 Hamilton Street is a very small 191 m² property, while No. 41 is 604 m², is potentially significant: it suggests that the present parcels may have resulted from subdivision of a larger historic holding.
I would pursue that next, including the 1840s Adelaide Street census records, historic maps and the original land grant/title if I can identify it. That is the route most likely to give us an actual name and date rather than an educated guess.