Below is the list of tables from the database along with their columns and datatype. Need to generate an accurate SQL query for the question.
Only use the columns present in the respective table. Only use the columns which are required to generate the SQL query. Only use table joins if required and not otherwise.

### Tables ###
TABLE: CREATE TABLE Dogs (name VARCHAR, dog_id VARCHAR, breed_code VARCHAR)
TABLE: CREATE TABLE Treatments (date_of_treatment VARCHAR, dog_id VARCHAR)
TABLE: CREATE TABLE Dogs (breed_code VARCHAR)

### Question ###
List the names of the dogs of the rarest breed and the treatment dates of them.

### Accurate SQL ###

SELECT T1.name, T2.date_of_treatment FROM Dogs AS T1 JOIN Treatments AS T2 ON T1.dog_id = T2.dog_id WHERE T1.breed_code = (SELECT breed_code FROM Dogs GROUP BY breed_code ORDER BY COUNT(*) LIMIT 1)