I had a look at the St Helier Baptism records (April 1817 to January 1824) at the Jersey Archive today. I found the following:
Page 101: 23-05-19 - MILLENER, SARAH, daughter of Richard Millener and Sarah, his wife. William Whitmore and Daniel Young, Stance Whitmore and Ann Young.
In the above, the date is presumed to be the date of baptism. I believe the names are those of the godparents. I am not quite sure why there are four of them. Normally there are two. I couldn't find details of any other births in St Helier around that time with similar surnames.
Then I checked the St Helier Marriages 1795 to 1824 and found this:
St Helier, 14-01-1819 - MILNER, Richard (Private 19 Regt. of Infantry) to BEER, Sarah (St Helier).
My understanding of this is that the first mention of St Helier in the extract above refers to where the marriage took place. I believe the mention of St Helier after Sarah's name is where she was born (although I checked back several decades earlier but could not find details of any baptisms in the name of Beer in St Helier). However, there was no place of birth mentioned for Richard in the marriage extract- just the reference to him being a soldier.
I had a quick look in some other records for more information on the regiments that were stationed on the island of Jersey at that time. Unfortunately, records for that period through to the 1830's appear to be missing, so you might have to do further research on that yourself. Certainly it was normal to have British troops stationed in the island at that time. Presumably France was still considered a threat. In fact, regiments continued visiting into the early years of the 20th century, long after the threat from France had gone.
From the closeness of the dates and the similarity of the names, it seems very likely that the marriage and the birth quoted above are linked to the same couple. However, the birth of Ann Milner remains a mystery. Could it be possible that she is the same Sarah Millener born in 1819, or could that be a sister of hers, or is she totally unconnected to the people above?
I should also just add that there are TWELVE separate sets of parish baptism/marriage/burial records. Doing a thorough check of all twelve parishes is too time-consuming. Therefore I cannot completely rule out that there is a birth record for Ann Milner hiding away in another parish register. However, I checked most of the parishes very quickly but could not find anything else of relevance in the name of either Milner or Beer. I just cannot say that there isn't a separate baptism record for Ann Milner with total confidence.
I also did a quick search of the 1841 Jersey census for anyone called Beer. There are a few people of that name, but I couldn't find anyone who might obviously be the parents or relations of Sarah Beer, whom I presume would have been born around the start of the 19th century, with her parents maybe born in the 1770's to 1780's.
Let me know if you can find out anything else of relevance. Perhaps Richard returned to England with his regiment at the end of their tour in Jersey? Are there any relevant military service records on ancestry? I am not a paying member myself so I can't view most collections. Could it be possible that Ann went to Staffordshire because that was where Richard Milner was originally from? Maybe his wife Sarah and daughter Sarah left the island with him?