Hi Garthkh, and welcome to RootsChat.
First if all, don't assume that spelling is important. Until the early 20th century it wasn't. Alick Cowie Frazer is undoubtedly the same as Alick Cowie Fraser. There's no such thing as 'correct' spelling, though Fraser is commoner than Frazer.
Secondly, don't rely on Google maps for anything serious.
New Pitsligo is mostly in the parish of Tyrie, which is south-west of the parish of Fraserburgh, though there is apparently a small part of New Pitsligo which is in the parish of New Deer. There is a Hanover Street in Fraserburgh (it's quite a common street name) so there is no reason to think that this address is in New Pitsligo, 12 miles away. If you have read this thread carefully you will have noticed another mention of someone who died in Hanover Street, Fraserburgh.
See
https://www.streetmap.co.uk/map?x=399560&y=867065&z=110&sv=hanover+street&st=6&tl=Map+of+Hanover+Street,+Fraserburgh,+Aberdeenshire,+AB43&searchp=ids&mapp=mapYes, Alick and Alex are both used as abbreviations for Alexander.
In Scotland, a married woman does not lose her maiden surname. It is customary to include her maiden surname on gravestones and in newspaper death announcements. In legal documents she would be named as Jane Cowie or Fraser.
In the 1861 census, Thurlaw Fraser, aged 34, married, miller journeyman, is at Little Mill in Ellon.
In the 1861 census, at Backhill, New Pitsligo, are
James Cowie, 60, farmer
Agnes Cowie, wife, 60
Jane Fraser, daughter, married, 26, miller's wife
Agnes Duff, granddaughter 5
Alex Fraser, Grandson, 8 months
all born in New Pitsligo except James and Agnes senior, who were born in Aberdour and New Deer respectively.
Alexander Cowie, son of Jane Cowie, was born in New Pitsligo on 23 July 1860.
So he looks very likely to be your Alexander Cowie Fraser.
In 1871 the family are at 54 Low Street, New Pitsligo:
Thurlow Fraser, 44; Jane, 33; Agnes, 15; Alexander, 11; Thurlow, 7; Jane, 5; Margaret, 3.
Agnes Cowie, born 26 April 1855, mother Jane Cowie, is presumably listed under her father's surname, Duff, in 1861, but in 1871 she is listed under har stepfather's name.
There are quite a lot of Backhills but I think the one where your Cowies were is here
https://www.geograph.org.uk/gridref/NJ8655 - Double-click on the map, then single-click again, to zoom in.
It's also on the mid-19th century map
https://maps.nls.uk/geo/explore/#zoom=16.1&lat=57.59383&lon=-2.21633&layers=5&b=1&marker=57.57130,-2.26079