Hmm,
Just created a second quick link and then took a look into the database table. It appears as though these are placed as a kind of pipe de-limited list like shown below
My Site|http://localhost:8888/test/index.php|1 Yahoo|http://www.yahoo.com|2
You could theoretically use a SQL query to append a new quick link to the end of every member row but you would really need to do this before the users add any in themselves or you wouldn’t know which number to add in at the end because if one member had added in a link as I have above then the next one would be 3 but for anyone who hadn’t added one in then it would be 2.
Probably the easiest thing to do would be if you perform the SQL query at the start of an install so that everyone has that quicklink as their standard one?
Also make sure you back-up your database first incase it all goes tits up! 
SQL Query
Can be performed by going into :
Admin->Utilities->SQL Manager->Database Query Form
UPDATE exp_members SET quick_links = 'My Link|http://www.mylink.com|1'
I’m pretty sure that should do it for you.
Hope that helps.
Best wishes,
Mark