This is quite common.
Sometimes, for whatever reason, baptisms were not recorded in the parish registers when they occurred. Probably not because of cost because fees for the recording of baptisms in the parish registers were only chargeable for a short time in the 1780s or 1790s.
When statutory civil registration began in 1855, people whose baptisms were not in the earlier records could have this remedied by a listing in the Register of Neglected Entries. Many people took advantage of this to ensure that they, or their children, were on record. The RNE is not an 'unofficial register'. It is an extension of the normal parish registers, and every bit as 'official' as those.
Birth was not the important date in the eyes of the church, which is why older baptism records often don't include the date of birth.
Mostly, however, the RNEs list birth dates rather than baptism dates because in the mid 19th century people could generally remember the date when a child was born, but not the date when they were baptised several years earlier.
In your case, it may be that the parents were among those who broke away from the Church of Scotland in 1843 and joined the Free Kirk. This is a common explanation for baptisms between 1843 and 1854 not being in the Church of Scotland registers.