Hi Jan,
I have found a family tree that has a Frederica Wilhelmina Carlqvist b 10 Aug 1805 in Vate. The following is according to this tree - her father Johannes Carlqvist b 11 Jul 1774 Alsheda, Smaland d 1844 Backs, Vate - her mother Cajsa Lisa Fagerhult b 10 Jan 1783 Lilla Ambos, Vate d 1840 Backs, Vate. Her parents married 18 Feb 1800 Vate.
Frederica Wilhelmina married Jonas Petter Blomberg 25 Jun 1826 in Vaskunde. He was b 9 Aug 1806 Kviungs, Stenkumla and his father was Niclas Jonsson Blomberg and mother Sara Christina Persdotter
They had a son Johan Petter Blomberg b 28 May 1829 Vate but the tree has no information about a wife.
I wondered if this might fit with what you have found? Also, I have not worked out how to show umlauts etc but there is an umlaut on the a in Vate and Backs.
Colin