I looked in Tice's book on buttons and did not see that button with a "Dowler Birminghman" backmark, and Tice's book is the most recent comprehensive book on the subject.
I believe MCGuinn and Bazelon list that mark as post 1900.
I recommend that anyone that deals with buttons at all get the Bazelon and McGuinn book. I don't know how much they are anymore, but its a good investment. Dowler DID make CW buttons, but the backmark was different.