Hi,
I can see Harry DUNNETT on the "UK, Dentist Registers, 1879-1942" at Ancestry between 1879 and 1905,
1879
DUNNETT Harry 53
1/
2 Ryland Street, Birmingham
Date of registration: 1878 Nov 5
Description and date of qualification: In practice before Jul 22 1878
1885, 1893, 1896, 1900 and 1905.
Same details, different address.
198 St Vincent St, Ladywood Birmingham
In 1871 Harry was living with his family and was a dentist's apprentice. He might not have had to qualify officially with exams as before 1879 dentists could learn just as an apprentice.
"Initially when the Dentists Register started dentists could register without a qualification if they could prove they had been working in dentistry for five years prior to 1878."
see,
https://www.bda.org/museum/enquiries/PublishingImages/was-ancestor-dentist/was-your-ancestor-a-dentist-factsheet.pdfRegards,
Daisy