She could but so would your adult cat. Depending on the vaccine neither of them will be protected from general infections. The concern would be rabies, but that depends on how prevelent it is in your area. It is unlikely that she will get anything, but try to find the mouse first.
Cheers
Kim
My daughter caught it in the `spider catcher` and took it outside, but it hardly moved so I reckoned it was in shock and would not live for long, I`m sure our cat must have injured it.