Later census have her born a little earlier 1842 I wonder if she was born just before the marriage and is under mothers name?
Is Hannah surname Waldron? **
There is a Sarah Waldron born Sep 1844 Stourbridge but again that was
after
the marriage so no need for her to be registered under that name

** sorry you said Hannah was Poole but I can't see that marriage in 1842

There are 2 Sarah Poole births in Mar 1841 Dudley but maybe too early.
Can we confirm the Joseph/Hannah marriage?