When are your ready to solo dive, only when you're ready to risk your life for a cheap thrill. Can you get a "card" to solo dive, sure, you can buy a card saying you are an instructor, or a "card" that you can do anything. No card can protect you in the water. . . there are some cards that call you a dive master, the navy offers that, It takes about 20 years and mastery of every commercial and military skill. That means a lot.
Why does every meaningful dive training organization insist on a dive buddy? Because of the total experience of millions of dives vs. the hundreds of diving deaths, when there was no "buddy" to help even a little bit. Jacques Cousteau and some of his divers started diving alone because there was only one regulator. As soon as there was more than one, they quickly knew they risked death if diving alone. Read his book "Silent World."
When I had only had a thousand dives, I made a dive with a friend with more experience, and he asked if I dove alone. I told him I, like many of my friends. would dive if an experience diver was in the boat, but not if there was no one along. He experienced a dive where the visibility turned to zero while he was down by himself. . . enormous numbers of fish were thrashing around, blocking the sun. They were in an illegal net dragging the bottom. He was tangled, and when he attempted to cut free, his knife was knocked out of his hand. He struggled against the weights of the net to reach surface. . . His soon to be fiancee, didn't swim, but paddled their anchored boat with a ski and reached him and held his head above water. Fishermen heard her screams and helped cut my friend loose.
You will choose to do what you want, and giving you some idea of how conditions can go beyond your control, even by the criminal act of others, not to mention all the things mother nature can throw at you. There are conditions where a bad dive partner can put you in danger. . . you can back away. There are many more situations where a dive partner can clear an intanglement on your back, share his air, bring you up if pass out, and more. . .
I've made a 1000 logged dives and a couple thousand without a log. . . I've got good friends that have over 50000 dives, and the idea of diving alone is not a good one. When you have that kind of experience, you have lots of people who will dive with you just to learn from you.
A common trick among hunters is to separate and go opposite directions, then about a third of the way into a dive, go look for the other to see if the hunting is better where he is. Or he will join you if you have found the fish. You need a lot of skill, and experience at finding your partner under water. . . but that is what lots of experience will teach you.
Sigh. 
It's not all that hard to find a buddy, so do a bit of legwork, and find one. It also enhances the enjoyment before/after the dive as you are sharing a unique experience.
