The Sächsische Landesbibliothek – Staats- und Universitätsbibliothek Dresden (SLUB) owns a manuscript (Mus.1-U-514) which contains works by Johann Christian Kittel. They range from very short preludes to elaborate sets of variations. This is one of the longer preludes. In the manuscript this piece is notated on two staves, nevertheless I think it should be played with use of pedals. Playing it this way has the added bonus, in my opinion, that the more interesting dialog occurs between left hand and feet.
The recording was done on the sample set of the Müller-organ in the Sint Bavokerk in Haarlem by Voxus Organs for Hauptwerk.