actually "funny" is the correct translation for the Arabic phrase and not "fun" Fun is a noun and we want an adjective here to describe the dog, so the dog is funny, and funny in Arabic is (if it means amusing) [ممتع]
If funny means (make one laugh) then it is [مضحك]
In the example sentence, 'fun' is actually an adjective which means 'enjoyable' or 'entertaining'. 'Fun' as an adjective doesn't necessarily mean 'funny'. 'My dog is fun' means 'I have a good time with my dog'.