"in doubt about" is correct and usable in written English.
You can use it when you are uncertain or unsettled about something. Example: I am still in doubt about what I should do next.
Nations go to war when they are "in doubt about which is stronger," he writes.
If in doubt about order of precedence, consult Debrett's Peerage.
He accentuates the positive, while leaving no one in doubt about the negative.
If in doubt about regulatory matters please contact your line manager or the managing editor's office.
The numbers can leave no one in doubt about the buyers' readiness to part with cash.
"Once they endorse, every day after, you will not be in doubt about who they endorsed".
And anyone still in doubt about the fact of climate change should read Kilvert's winter entries.
So when in doubt about acidity, use cream and lighten the base with milk later.
She retreated from him somehow without letting him ever feel in doubt about her love.
Mr. Bellow himself, Mr. Atlas shows, was never in doubt about his talent.
If in doubt about borderline inappropriate stuff, better to err on the side of caution.
