Rinse the dwarf oranges, rub dry and finely dice them, removing the seeds. Place kumquats and the jelling sugar in a large enough bowl, mix well. Cover well and set aside for 3 to 4 hours. Place kumquats and jelling sugar in a large saucepan. Add rum, lime juice and vanilla sugar. Bring everything to a boil and continue to boil for 5 min, stirring until bubbling.
Fill jam into clean screw jars. Immediately turn upside down and set.