|The name is not perfectly legible, but it appears to be
Perhaps Louisa means the farm of Jacob Shafro (or, more correctly, Shaffroth)--which is situated on the east side of the Windsor Road, about a mile north of the Blue Bell Inn (which latter stood at the southeast corner of present Windsor and North Streets). If so, then it would seem that the girls consider three or four miles--the distance from Beamishes' to Shaffroth's farm--no great distance ("went but to Shefrow's"), unless the adverb is meant to emphasize that this is the day's only activity, that (unlike yesterday) they did nothing this morning or earlier this afternoon.
(Things would make a lot more sense if the phrase were "out to Shefrow's," rather than "but to Shefrow's"--which is possible, although the first word of the phrase does appear to begin with a "b" rather than an "o."
Jacob Shaffroth is about 49 years of age.Bapt. 20 Dec. 1767, the son of Johann Georg Schaffroth--who in 1751, at age 20, settled in Halifax after arriving on the Gale from Erigen--and his wife Christina Schaffroth. M. Anna Christina Kaulbach, b. ca.1770. (She d. 4 April 1821. He d. 9 April 1826.)
(It's likely that the Beamish girls know Jacob Shaffroth's daughter Elizabeth, for just three months later, on 4 Jan. 1816 she will m. John Peeples, the Beamishes' next door neighbour.)
If it was to Shaffroth's they walked this day, perhaps they started out in the direction of the Governor's North Farm.
"Another road [in addition to the road leading to Point Pleasant], leading to the northern suburbs, also became a fashionable resort. This was made under the auspices of the Governor, Sir Andrew Snape Hammond, and formed part of the highway to Windsor. The fact of his residing on the road, in a house erected on the western boundary of the Governor's Farm, (near the head of the present road leading from the Richmond Railway station,) tended greatly towards rendering it a favorite walk. Near his Excellency's dwelling stood another, which becme famed for breakfasts and suppers during the summer season. Not only did gentlemen walk out in the afternoon and order an early dinner, but it was common, and one of the most popular modes of spending a holiday, for ladies and gentlemen to form a party, and start early in the morning that they might breakfast, dine, and sup, at one or other of the "tea-houses," as they were called, which were kept in various parts of the peninsula." (Hill 1864 , p.34)(To view a plan showing location of Jacob Shaffroth's Farm, click Halifax-Dartmouth, 1815 .