There's no downloading (do you really mean "importing"?) needed here.
Once you change to your own Creative Cloud account on the same computer, you shouldn't have to do anything other than start LR and your catalog showing your images should appear.
All is working transparently. Even the preferences will be taken over. I switch regularly between my company account (full CC subscription) and my private account (Photographer's plan). There is simply no difference, except that on the personal account, I cannot use InDesign or Illustrator etc.
I even have an external harddrive, that I plug to any computer, and the LR catalog on that harddrive is usable from everywhere.
Go ahead and do as you planned. Your usual applications will work under any account. Only the additional applications will need your new account.
Just to be sure: Sign ins need to be different! 2 Adobe accounts will be needed (but at the end, as long as your subscription to the full CC is active, you will use only that one).
Yes Sign Out of your brothers account and Sign back in using your Adobe ID account that you used to purchased the subscription with.