You've received great responses so far. I especially second what puffin and Platypus101 shared.
I'll just add that many auto-didactic (self-taught) kids learn things the way they see them and may benefit from being shown the way something is typically done. This may be especially true with printing. Since she is practicing her printing by writing her name on many things, she seems to enjoy printing and this may be a great time to coach her on printing left to right. Practice paper which shows the formation of each letter in stages (sometimes with tiny arrows and numbered strokes) may be helpful.
When you read aloud to her, you might want to consider moving your finger along the words on the page from left to right so she can get used to seeing the progression of words from left to right.
Somewhat related, auto-didactic kids who later acquire new vocabulary through reading alone (rather than also hearing the new words in conversation or being read aloud to) may mispronounce words and therefore may not recognize a word when they do hear it. Kids are typically not as successful when they are completely self-taught as they may at some point need to unlearn a portion of what they've acquired.
