Thanks for writing. You can transplant Knock Out roses anytime of the gardening season from spring to fall, though the cooler months of spring and autumn are the best time.
The best time to prune your roses is in spring --- March or so just before or as the new growth begins to develop.
Knock Out roses are patented varieties, so it is technically illegal to try to propagate them, so I'm really sorry, but I can't publicly offer advice on how to take starts from the plant.
---Justin, Senior Garden Editor, BHG.com