births would not be officially recorded until later in century - usual approach was baptism within the first couple of weeks at this period - so unles you can find a private record unlikely you will ever determine it.
Agree Robert was active in Douglas - however he may have not wanted to stay in Santon - remember that James Moore had been a merchant in Douglas (his first 6 children bapt there) and refered to as Mr James .. so moneyed - removed back to Santan post revestment - Robert was well down pecking order to be left property.