Newbies can not have avatar/profile picture.
There is a post about it however I do not know which one. As far as I know, to have a profile picture - you will need to be at-least a full member rank.
Yes, only Full members and above can use an avatar. Maybe the following quote from Theymos can complement your answer:
How does one become a full member?
To become a Full Member, you must have at least 120 activities and 100 merits.
Merit & new rank requirements