First, remember that a DBA is not a legal entity. Your profits, any legal issues, etc. will flow to the parent corporation. And, in some states, you have to use the parent`s name when referring to the DBA. For those reasons, I think of the DBA as a marketing or branding tool, not a financial or legal tool.
With that said, having a separate bank account is not a bad idea as long as you understand that in doing so you are not protecting the assets of the parent corp. In terms of QuickBooks, I would most likely keep one file - since the parent corp will consolidate the DBA for most tax and financial purposes - but use a class so that you can report on the parent and DBA separately for management purposes. If having one file would make product, client or vendor lists to long and there is little overlap, at that point, a separate file would make sense.
This is not legal advice (I am not a lawyer) but some of my clients in this situation, set up an LLC where the parent corp is the sole owner. The parent corp would have better protection than a DBA.