Robert Gibson Howkins was obviously named after his grandfather Robert Gibson who died 12 years before the grandson was born.

The IGI lists a Robert Gibson Howkins christened May 31, 1835, Holy Trinity Clapham Surrey, father Theophilus Howkins, mother Marian.

Parish Records Holy Trinity Clapham
Robert Gibson Howkins baptized May 31 1835, parents Theophilus and Marian Howkins, abode Clapham, father’s occupation Gent.

England Select Deaths an Burials
Buried May 3, 1836 Robert Gibson Howkins, age less than 1, St. Mary, Warwickshire, England

Parish Records St. Mary’s Warwick, Warwickshire
Burial May 3 1836 Robert Gibson Howkins, abode Market Place, age infant, ceremony performed by

From the Historical and Descriptive Guide to Warwick Castle, Beauchamp Chapel.
St Mary’s Church
The Choir
Near to the altar, floor, north side.
Robert Gibson Howkins, who died Apr. 25, 1836, aged 12 months.
[This is the same church his sister is baptized and his grandmother Anne Gibson nee Woodin was buried later]

A thumbnail image of his grave monument is available at gravestonephotos.com

Note the Choir of St. Mary’s Collegiate Church contains the grave and effigies of Thomas Beauchamp https://kimsimmonds.net/ps01/ps01_492.htm

Also note: 5 years after his death his parents were living at Harbury which is about 8 miles from Warwick. Possibly they were living in Harbury when he died or perhaps they lived in Warwick and moved to Harbury.