Jonna, I'm not sure how soon you can separate pups from the parent, but I generally wait until the parent plant starts to look scruffy. That usually indicates it's finished making pups. Then I roust the whole plant (they are so shallow-rooted you really just lift them) cut off and throw the parent plant - they only bloom once, so it is done - and place the pups in its place. Mine definitely bloom best if I keep them thinned out.
This timing - getting scruffy after blooming - varies by variety and yours still look beautiful.
If you are anxious to increase your clump of broms, you could probably separate the one pup on the left of the second picture, it's almost as big as Mama already! I use a small serrated knife to cut the umbilical, and wear gloves with long gauntlets to protect your arms from the leaf edges, they can be sharp!
