Hi there,
I don't have a Jessie Brown in my tree, but I can maybe offer some tips on searching for her. Jessie, rather than being a name in its own right, is often used by people called Janet (possibly also Jean or Jane) so searching for one of these first names may help.
However, it will still be a very common name. Do you have the names of her parents to help you narrow things down a little?
Cheers,
Clare