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'child born in absence of husband', would this mean the child is illegitimate or that the child is the husbands but he's gone?

There are a few other baptisms with similar wording....

1844 Devon - "A Notorious Adulteress This Being the Second Child Born By Her During the Absence Of Her Husband At Sea"   

1805 Berkshire - "This is a spurious child born during her Husband's Absence"

1834 Wiltshire - "Born in sailor husband's absence; not his child" 

Illustrated London News
06 January 1894

I am wondering if records for the Royal Artillery will reveal the activities of the regiment and thus where at sea Charles was born.

Do you know which Company of the 8th Battalion Peter served with?
The link below gives a table of the 19th century stations for the 8th Battalion of the RA.

Scroll down to Chapter VIII then to page 140 onwards. Page numbers are on the right.

https://www.gutenberg.org/files/58209/58209-h/58209-h.htm

You could always purchase the 1874 Baldwin/Allen marriage cert, in order to confirm his details.
William's occupation may help to locate him in the 1881 census onwards.

Frederick Allen could be fictitious. Someone Amy invented. Who knows.

Sounds like William Baldwin was out of the picture, considering Amy is listed as "spinster" when she married Thomas Reeves in 1878. Makes sense that she married Reeves elsewhere (Notts).

1891 census - Havelock Place, 5, High Street, Upton with Chalvey, Eton, Buckinghamshire

Amy and Thomas Reeves, plus three children (including Gilbert Allen).