When should someone start doing tournaments? (when are you considered good at chess?)

Prepare openings, solve puzzles, understand tactics and keep playing. Also analyse your mistakes and try not repeating them. You'll get there eventually. As per tournaments are concerned, you can start anytime. There are tournaments for all levels. Find one that have players within your elo range.

You got it wrong. You don't play tournaments when you become good. You become good when you start playing in tournaments

You should start playing in tournaments when you are interested in playing in tournaments. There is no minimum skill level required. However, you should be prepared to lose many games while your skill level improves.
When can I say "I'm pretty good at Chess."
There are basically 2 ways:
1) When you've met the goals you set for yourself.
2) When you're one of the best players in your age / region.
As for tournament chess, it's for everyone. Find a large tournament where there are sections (for example U1000 means players rated under 1000). Enter the section you belong in and have fun / learn.
In my first OTB tournament there were a few GMs, but there were also tons of people below 1000.
I am not new to the game in any sense of the word. I have been playing it since my dad taught me on Christmas day when I was about 6 or 7. I have loved it from that moment onward and have had a strong relationship with it since. With that being said I suspect I have never actually been "good" at it. I have used a lot of different chess software over the years and have hovered around 900-1200 for most of that time. So when should I consider myself good enough to start playing in tournaments? When can I say "I'm pretty good at Chess."
Full disclosure a lot of my chess games are online or against computers. I do not have a lot of playtime with actual people face-to-face. This is the biggest reason I ask this question.