Baptisms of Jacob /James McGough 28th April 1890 (workhouse) & 10th August 1890, both in register of St. Mary of the Assumption, Burnley were exactly the same as Agnes. Compare them with these 2 baptisms in the same year of the register: Catharine Lee, 1st March, abode workhouse and John Douglas, 9th March who have only 1 entry each, although it looks as if they also had 2 baptism ceremonies.
The baptism on 13th December of Agnes would have been a simple rite done at short notice. A baby who was gravely ill, in danger of death could be baptised by a lay person if there wasn't time to fetch a priest. The words "in periculum" signifying the child was gravely ill might be written on the baptism entry.
Another possibility is that a priest routinely called at the workhouse and carried out quick baptisms on babies there . When the family was back home they took the baby to church for "the full works". This is just a theory of mine. While looking at a baptism register for my own village I noticed that babies from the workhouse were baptised on the same day. It was a tiny cottage workhouse, a mile from the church. So I wondered if the parson went there to baptise the babies.
I see Agnes had a godmother at her 2nd baptism.
If you browse the register of St. Mary of the Assumption you will probably find more examples like those above.
Burnley Workhouse records have only been on Lancs OPC for a fortnight.