A. What are you two doing? OK B. We're just HAVING some friendly chitchat. or We're just chatting.

It's fine.

A: is correct. B: Either; "we're just having some friendly chitchat." or "We're just chitchatting." * The sentence "We're just doing some friendly chitchat." sounds awkward since we do not use the verb 'to do' when referring to conversation, rather we use 'to have'