It may be that any record which may have existed has not survived.
Try
www.scotlandspeople.gov.uk to see if there is a baptism entry in the Church of Scotland parish register.
If not, then it is possible that he (or rather, his parents) may have been (an) adherent(s) of some other denomination than the Church of Scotland - Free Church of Scotland, Episcopal Church of Scotland, Roman Catholic, or any one of many others.
There are some records of other denominations in the National Archives of Scotland
www.nas.gov.uk but many, notably most Episcopal and RC records, remain with the churches.
I see that the IGI lists a marriage in Montrose in 1847 of David Herschell to Janet Davidson - could they possibly be Alexander's parents?