I think 1946-47 is rather too early. Remember that IOTL the Soviets did it by 1949 only through a great deal of stealing Project Manhattan data. ITTL the Soviets are the enemy so potential Soviets spies and Communist sympathizers in Britain and America shall be hunted down and rooted out much more efficiently and ruthlessly. Yeah, ITTL the Axis is pooling the efforts of German and Soviet research teams (and the Italians had some kickass nuclear physicists, too), they have many more combined industrial resources with much less destruction than OTL. But even if Goring shuts down the harassment of Jewish scientists in 1942, all of them had already fled continental Europe and they aren't coming back.
I think that the Axis could likely develop the bomb by 1948-49 if Axis leaders don't get aware of Project Manhattan (see above why Soviet infiltration ITTL cannot be taken for granted), by 1947-48 if they do and make it top priority. However, even if they don't manage to do it, remember that potentially the Axis can still field a rather effective MAD deterrent against the Allies with chemical and radiological bomber and missile warheads. If they realize they can use them, they shall have both of them available by 1945, as well as the delivery capability to turn Britain into a wasteland and hit the East Coast of North America seriously. They have the industrial capability for that.
And don't forget the combined power of the German, French, Italian and Soviet air forces which are focused west ITTL. Look what they're doing to the bombing campaign at this stage of the TL. They're inflicting some huge losses since they've managed to keep air superiority. How big are the chances of one bomber getting through the air defences of western Europe all the way to Berlin, Dresden or Hamburg with German mass produced jet fighters patrolling the skies and (likely) Germany having radar by now?