No, infact you have it backwards. If the peak of the roof runs say from
side-to-side of the house, then most likely your joists run
front-to-back (part of their job is to tie the opposite eves of the
roof together, else the eves would spread and the peak would collapse
flat). So your wall is perpendicular to the joists, most likely, which
generally hints that it is load bearing.
Doors have nothing to do with anything, and neither does the length of
the wall. A wall just 1/2 a foot long could be critical, depending on
the construction. (aka, a post).
You can get a better idea by looking in your attic at the joists, and
even try to see how the various walls are attached.
On the other hand, some roofs are designed to span the whole distance
without support. It is hard to tell from here, but it sounds like it IS