SQL query for parent children relation

I am trying to write a sql query on bellow table.

╔════╦══════════╦═══════╗======╗======╗
║ ID ║   NAME   ║ CLASS ║PARENT║ DOB  ║
╠════╬══════════╬═══════╣======║======║
║ 1  ║   DAVID  ║ SPIN  ║      ║1     ║
║ 2  ║   AROON  ║ BIKE  ║ 1    ║1     ║
║ 3  ║   LEO    ║ YOGA  ║      ║2     ║
║ 4  ║   LIN    ║ CYC   ║ 1    ║2     ║
║ 5  ║   STEFA  ║ YOGA  ║      ║3     ║
║ 6  ║   GLORIA ║ RUNN  ║ 1    ║3     ║
╚════╩══════════╩═══════╝======╝======╝

And, output for this table should be like following

╔════╦════════╦═══════╗======╗======╗
║ ID ║ NAME   ║ CLASS ║PARENT║ DOB  ║
╠════╬════════╬═══════╣======║======║
║ 1  ║  DAVID ║ SPIN  ║      ║1     ║
║ 2  ║  AROON ║ BIKE  ║ 1    ║1     ║
║ 4  ║  LIN   ║ CYC   ║ 1    ║2     ║
║ 6  ║  GLORIA║ RUNN  ║ 1    ║3     ║
║ 3  ║  LEO   ║ YOGA  ║      ║2     ║
║ 5  ║  STEFAN║ YOGA  ║      ║3     ║
╚════╩════════╩═══════╝======╝======╝

So this is the explanation of the output
First parent David as his DOB is 1, 
--David three childrens sorted based on DOB
Then LEO as his DOB is 2
-- Leo do not have children[if he did, would be here as sorted on DOB] 
Then Stefan as his DOB is 3
--  Stefan do not have children [if he did, would be here as sorted on DOB] 

So what i tried?

SELECT * FROM user group by ID, PARENT ;

Above SQL, statement return items in parent children group but not doesn't maintain any order, when i add ORDER BY, SQL doesn't seems like honoring GROUP BY anymore.

Then i tried to do joining and end with two complete different tables where one contains all the parents and another one contains all children. UNION ALL on that two query returned expected data set but not in expected order.

Any thoughts?

UPDATE

Output should be
Pick first entry which doesn't have any parent.  
--use that id and find all of its children and placed them in sorted order
repeat for every row in the table

Note:

--parents are sorted based on DOB
--child's are also sorted based on DOB 
--DOB are valid timestamp 
--PARENT, ID field both are UUID and define as CHAR