Dandruff

You could try bathing her less, like only when she's truely dirty and add 100% Salmon oil to her food. Sometimes the cold months + heat on in the house dry out my dogs skin (like it dries out my skin).

I will add that I very rarely bath Apollo...like maybe only 1-2x a year, or only if he's dirty. Instead, I just brush him, and if I want him to smell less doggy I use some pet safe cologne (bought mine at the groomers). He's a Lab though, and I know they should only been bathed with shampoo extremely rarely. Patty & Molson (Cockers) are bathed every 4-6 weeks when they need to be groomed.

Prednisone on a regular basis is *very* hard on the liver and kidneys both of which have a huge amount to do with the skin.  If she's on pred regularly then honestly dandruff may be the smallest of skin issues she may have. 

You may want to look into other possible treatments to take the place of the pred (I've no clue what it's for - unless this is the one with immune-mediate polyarthritis).  Sorry -- this IS the voice of experience talking here ... I've got scads of experience with the stuff for all sorts of different reasons/uses.  It's very likely it IS the culprit here.

There *are* other solutions to weaning her off the pred onto something less damaging OR I can give you some pointers on what to do that will help protect her body *against* the pred -- particularly the liver and kidneys.  Remember, Billy had IMHA so I'm no stranger to immune-mediated stuff and I have Rheumatoid arthritis myself (which is also IM).