If you let her have the kittens she will have to wait until they are weaned to be spayed (8 weeks). If she looks like her sides are sunk in and she is skinny, she is not in very good shape to nourish a litter of babies. As sad as it is, I would suggest going ahead and having the vet spay her now.
Wanting to foster a litter is a great idea, but if you are working at a vets office I'm sure another cat who is too far along to spay will show up soon, and you could offer to foster her. Or call a foster agency to see if they need help. The agency I work with pays for vet care until the animals are adopted, which is a great help!
How nice of you to take this cat in and care for her!