Hi Ivor and welcome to RootsChat

I'm no expert on Romany families, but I have found the following baptisms to Isaac and Sarah Whitcher:
Betsy b 2 Mar bapt 31 Mar 1802 Eling
Charlotte b 24 Mar bapt 9 May 1804 Eling
Harriett b 25 Apr bapt 10 Sep 1806, Eling
George b 2 Sep bap 26 Oct 1808 Eling
As you say no sign of an Alexander, but they seem to have stayed in the Eling area for a number of years.
There are two marriages recorded for an Isaac Whitcher:
Isaac Whitcher m Joanna Wade 3 Dec 1766 Eling
Isaac Whitcher (widower) yeoman m Sally Hatch 17 Aug 1797 All Saints Southampton by licence
No idea if they are the same Isaac

An Isaac Whitcher was buried in Eling 18 April 1815 aged 73. A Johanna Whitcher was buried in Eling 22 May 1794, no age specified. Isaac left a will which was proved in 1817, copy at Winchester.
If the second marriage is for the parents of Alexander then logically he could be the first child, given the date of the marriage. However, Romany family does not seem to match with yeoman.
What evidence do you have that Alexander's father was Isaac?
Nell