I saw a similar word order in the -DIk skill:
"Benim sevdiğim adam o." - "He is the man I love."
I think someone wrote that "O benim sevdiğim adam." was also right. I suspect here "Bu dün beni öpen kadın." wouldn't work, because the relative clause starts with a noun (dün), so there would be a confusion as to whether "bu" is attached to the noun or not. Although in this case "bu dün" - "this yesterday" doesn't make much sense.
Also, are both "bu" and "dün beni öpen kadın" subjects? Referring to JohnH14's comment about the SOV order.
Actually, both ways are perfectly fine.
1) "dün" isn't a noun, it is an adverb (yesterday is an adverb as well). 2) Both "bu" and "dün beni öpen kadın" are nominatives meaning that they are just connect with the verb "to be." There is no direct object.
This word order just sounds a bit better, but both ways are fine and are already accepted.
In Turkish, relative clauses cannot finish off a sentence because relative clauses must attach to the subject, indirect object, and/or direct object. Thus, SOV word order is preserved. For example, "[I saw] [the man who you talked to yesterday]" would be translated as "[dün seninle konuşan adamı] [gördüm]." Because, for any sentence with a verb, relative clauses cannot be at the end, I suspect that the rule stays true for sentences without a verb (i.e. bu köpek iyi) to preserve the style. This is just a guess; hopefully someone with education in Turkish grammar could tell us the correct reason.