That's right, it's the leading attributive clause. The infinitive after is is the object of the clause, so this sentence is correct.

Today is the 20th birthday of my friend who came to Singapore with me. This sentence is wrong. The clause of this sentence is equivalent to "my friend is going to Singapore with me." In the attributive clause guided by who, there are two predicates, one is and the other is come, so it is wrong and should be removed.