You have to use your own device or you will lose access to the data saved for that device. Your brother may have already messed this up and that is why you are getting the message. From my own experience, upgrading from the DS to the 3DS I lost all my friend contact info, but I do not think I had synced with the Dream World until afterwards, so I am uncertain as to what it would do to your comatose Pokemon.
In general, since there is only one save file and can only have one device registered, you shouldn't share Pokemon games unless the other person is just playing musicals/movie-making/catching Pokemon after you beat the game.
This is a really annoying concept for Dream World. Even something as simple as changing the time can cause sync issues and forces you to wait at least a day before gaining access again. I'm disappointed they did not do anything to fix this in Black 2 or White 2. There are valid reasons to changing your time. My DS Lite doesn't change time for day light savings and that caused my original issue.
Your best bet is to get the card back in the original device and wait for it to sync up again. Once you get it sync'd up take your Pokemon out of sleep and then switch devices. This way you won't lose anything.
switching devices wont make you lose any DW pokemon or info, but all your FC will be deleted. That's what happen to me. You may get an error, but all you need to do is re-sync to the dream world and if the energy drains out just wait till the next day.
The Pokemon game files are HUGE in comparison to other games. Unless they had a system set up to let you save to the DS, then that would not be possible. Really, if Pokemon would make the move to the 3DS, then a system like that could quite possibly be put in place.