Yes.  Give her 2, or even 3, litter boxes in a row.  One of my cats did this
when she was young; the lined-up-in-a-row litter boxes solved the problem.

Cathy

--
"Staccato signals of constant information..."
("The Boy in the Bubble")  Paul Simon

This almost always means the cat needs a separate box next to it to poop in.
Some are funny that way and like separate boxes for separate operations, so
to speak. Especially as she is in a new environment, it could really make
her feel better about everything. Also, I would scoop at least once a day as
she sounds like she doesn't like even the possiblity of stepping on "icky"
while she goes. Cats can be extremely particular in their bathroom habits.

Karen

I would like to reiterate what the others have said -- get another litter
box, and place it next to the original one.  I sometimes say that my cats
"specialize" because they will use one box for feces and the other for
urine.  Oddly, they will sometimes trade boxes; the box that is used for
feces one week may be the box they use for urine a few weeks later.  Mine
don't use either box *exclusively* for one purpose, but there is a clear
pattern.  Incidentally, I have one box in one room and the other box in
another room; but the recommended solution for a problem such as yours is
usually to place the boxes side-by-side (or at least close together).
Later, you may be able to place the boxes farther apart, if you prefer it
that way.

MaryL