Thanks to you both. I guess I get the picture of baptism at home. I knew it was allowed in cases of sickly infants at risk of not reaching the church in time. The other "proclamerch" on the page also has the home baptism phrase before the child's name. I'm just surprised I never noted it before, or saw an explanation in the guides for reading kirkeboekke. Possibly the marginal note is a "proclamation" of the previous baptism, and no repeat of the ceremony took place in the church. The word could be derived from the Latin "proclamo".
The good news is that little Inger did live to adulthood.