The moment you have created your work, its copyright is legally yours. You don't need to do anything official, not even putting the little (c) sign on your work (although there's nothing to stop you, but a publisher's editor is likely to have a bit of a laugh over it).
Any reputable publisher would not dream of stealing your work. However, there are enough disreputable publishers out there to be worried about. Any decent writing forum's members will advise you of the 'predators and editors' of the publishing world.
If you want to take more concrete steps to protect your work, then committing it to your PC or one of the above mentioned forums will put a time stamp on it that could be used as evidence if someone did try to steal your work. Another method (and probably good for your own peace of mind if you don't trust computers) is to seal a copy of your work in an envelope and post it to yourself, leaving it sealed (with a postmark on it, of course) when it's delivered.