Can my 6 week old baby girl gets deathly ill, if I kiss her while I have a cold sore?

Yes. You can easily transmit the virus that causes cold sores to a child by kissing them when you have an active sore. Although "deathly ill" is not a true medical term, and therefore i don't know exactly what you mean by this, i can tell you that kids can get pretty sick. They can get oral herpagina/stomatitis which can affect their whole mouth and lead to difficulty eating and lots of pain.
Conceivable. But not likely. Most humans acquire herpes simplex virus from contact with others. It is possible, particularly in a 6 wk old to get a severe primary herpetic illness, but also possible that the passive transfer of partial immunity from mom during pregnancy will protect her. It is rare to see herpes meningoencephalitis from this type of contact, but not impossible.