The stamp is indeed from the Hyderabad SG O41 family, the Official overprint on the 1915 1 Anna, and Gibbons does indeed offer 'carmine'and 'scarlet' as shades. The carmine and scarlet are normally perf 13½ and catalogued at 10p each; carmine perf 12½ is £3.50 and perf 11 15p; scarlet perf 11 is £32.
I suspect there are more than two shades of this stamp, but this

I rate as the scarlet, and this

I rate as the carmine shade, so yours probably belongs among the scarlets.
These are mint copies of the unoverprinted stamp, so one can see it a bit better:

1 Anna was the workhorse, basic letter, rate for year in Hyderabad, and the government made just as heavy use of them as the general public.
It's a nice point that Hyderabad, being the biggest of the Indian States, had negotiated a special deal with the Imperial authorities that allowed its Official mail to be carried by the Indian mails
outside Hyderabad, at Hyderabad postage rates. Hyderabad was the only Indian State to be allowed this privilege. Unfortunately I don't have an example with your stamp, but here is a later cover sent from Hyderabad to Indore - which was a State in its own right, and definitely outside Hyderabad State:


You'll notice the same black Service overprint on these stamps, and your 1 Anna.