Hi Arremin -

The sooner you can start learning and playings songs the better! That's what it's all about afterall... It will help firm up some of the things you've learned because you get to put it to practical use. It's also fun!

In my opinion, it's good to go through learning material like GF1 and learning songs in parallel.

Eventually you'll be able to play without looking at your hands, but it's OK to do while you are learning a song. Even after you know the song, you may look down at certain points to make sure your hands and fingers are getting to where they need to be.

Congrats on your progress! You are doing quite well if a month in you feel ready for songs.

Have fun!