It seems strange to me that the second name of Jane does not appear on any other records.
Hi Marj
It's entirely up to you of course, whether you wish to purchase this birth record.

I agree, it is strange that the second name of "Jane" does not appear on other records, but this sort of thing is not entirely unheard of. [I have a g/grandfather whose second name was not used on his marriage or death certs. and yet it appears on his children's birth and marriage records and his wife's death cert. Jolly annoying as he had a frightfully common Scottish name and I still haven't found his birth.]
Perhaps it's worth sending a (cheeky) email enquiry (re: "Susannah Jane McCORMICK - 1871") to BDM - prior to making a purchase ?

Tell them (only) that you have a "problem" with the spelling of the surname "McCORMICK (as opposed to McCORMACK) and ask them to check their records. Also advise them that the mother's name is "Harriet". Ideally, they should be in a position to at least confirm whether "a Harriet" was the mother of the Susannah Jane.
~ Lu