This question already has an answer here:
I opened Cairo-dock in my terminal with:
open cairo-dock and that worked but if I close the terminal it goes with it. How can I keep it open regardless of the terminal?
Yet another way:
In the bash shell, the disown builtin command is used to remove jobs from the job table, or to mark jobs so that a SIGHUP signal is not sent to them if the parent shell receives it (e.g. if the user logs out).
I personally use screen for this kind of stuff.
What's good about this is that if you want to terminate cairo-dock, you can reconnect to the screen session and terminate it.
Screen has other uses. It's a terminal multiplexer.