Sorry don’t have specific experience of Dulwich but do appreciate your dilemma.
I’d say: Accept only if it takes away 11+ pressure, and you want to stay at Dulwich until 18, otherwise I think too disrupting.
Things to think about, that I hadn’t realised before going through similar (we stuck with state): Year 6 at their old state primary is great fun for the kids.
The fact that your DS passed at this stage suggests he will pass at 11+.
In your shoes, I would not accept, I’d reapply at 11+, but with careful prep (don’t sit on laurels, it’s very competitive at 11!).
Apply to one or two from the big 3 - kings Wimbledon, St. Paul’s boys, Westminster.
Be aware that City throws out some 11+ curve balls!
I know DS who didn’t get an offer there, despite scholarships from the big 3.
Then I’d include one or two easier schools e.g. trinity, dulwich, Whitgift.
I’d be amazed if he didn’t get offers at 11+!
On the other hand, it can be tough going to one of the very top academic schools from state (it’s quite full on in y7, as the state kids need to catch up! Also state kids are not used to the level/speed of work. I had not appreciated that!).
That said, while year 7 may then be quite a tough adjustment for your child (or at least not as easy as for the prep school kids who have - in our case - already covered much of the syllabus e.g. Latin, the sciences) worth saying that my child enjoys the academics and is doing just fine. Not top of class tho (something he used to enjoy, I reckon!). But I am confident he will start flying ahead as he catches up! Your boy sounds the same.
One last thing before you turn down dulwich and go for one of the super-super academic schools: think about whether your son will be ok NOT being top of the class (something he’s prob always been without much effort). Will it be demotivating for him to suddenly get lower scores in tests than some of his friends? (& omg there is constant testing!)
Bottom line- join dulwich now if you can see him being there for the duration (& it’s obvs a very good school). Or go for one of the top academic schools next year = enjoy year 6 (not to be underestimated!) and potential of a more fast paced school for secondary. All the kids who passed 10+ seemed to get into top academic schools at 11 (anecdote!).