Anything created - be it art, a song, a book, computer code, a photo - has a copyright automatically in favour of the creator.
It is not uncommon, in some industries that commission works, to specify in the contract the specific uses of that work. Can it be used for marketing? On TV? Without credits? Viewable by the public? Can it be reproduced in any form?
It is also not uncommon for companies to request a "buy-out" of the intellectual
property/copyright. This usually attracts significantly higher fees. For instance, a photographer takes a shot of a celebrity. Your newspaper wants to run it. He may allow them to use it for "any purposes" for a fee (and usually will because it will go public), or he might barter specific uses (not on the website, for instance). He might also bargain hard to keep the rights to sell it to another newspaper.
In your case, there are small ways to improve your situation.
1) In the contract, there is a probably a clause about your company providing the brief. Hence you own the concept. Tell her you will get is drawn elsewhere.
2) You might, in your brief, require your company logo. Which is copyrighted/trademarked to you.
At least in these two instances, she cannot use the work for anything either.
3) You tell her you want exclusive use for...
- , and offer a reasonable fee. Then tell her that more work will come her way if her fees and conditions are reasonable. Even agree a much higher fee for using it in instances you haven't specified.
