I will divide this answer into two parts: 1st, what you are supposed to be as a DM and 2nd, when I believe one is ready to take the big step. Please consider that I am not a dive professional, so my ideas may be biased - professionals know it better than me.
1 - DM/DL
First of all, different agencies have different regulations and different names. Here in France, the equivalent to a DM is "Niveau 4" (N4), equivalent to CMAS****. In most European countries, the equivalent to DM is the third level diver, or equivalent to CMAS***. With most American agencies, you have the Dive Master certification, Dive Leader, or something similar. From now on, I will only use the word "DM". What do these DMs have in common? They take responsibility for other divers. As such, depending on the country regulations, you might be held liable for accidents.
In general, if an accident happens, you should prove that your response to the accident was appropriate. Here we enter into the legal aspect, which I am not going to cover. So let's move on. In general, I can think of three different kinds of inconvenient that can trigger an accident:
(A) inconvenient that you can solve with skills, such as currents, low visibility, typical environmental issues, etc.
(B) inconvenient that require interactions with other divers: out of gas scenarios, exhausted people, bad etiquette divers, etc.
(C) extreme events: unforeseeable extreme environmental events (never heard about it actually can hapen), panicked divers, serious injury, unconscious divers, etc.
Group (A) comprises things that are manageable with good skills (when they become unmanageable, they move to group (C)). As a DM, you must manage them, period. No excuses. If one day you don't feel well or for any reason, you think you are not able to manage them, do not dive.
Group (B) includes things for which you have extensive training. You are supposed to react appropriately and efficiently and, if the other diver(s) do not respond in an "extreme unforeseeable way"***, you are supposed to solve the issue. The management of these kinds of scenarios includes the abortion of the dive.
***"extreme unforeseeable way" = deliberately not listening to you or getting panicked; both these reactions would move this scenario do group (C)
Group (C) includes things that, unfortunately, you can only partially manage. As a DM, you are supposed to react to put as many divers as possible in safety. For injury and unconscious divers, you should have the training, and you are supposed to respond as to standards. For extreme environmental events, prevention is the only weapon: avoid going to the sea if you expect a thunderstorm. Panicked divers and people who deliberately don't listen to you: well, here really depends on the situation, the only constant is that a DM must be proactive in solving the issue.
2 - When are you ready to be a DM
For sure, you need the training, but is that all?
Before becoming a DM, you need to ensure that your skills are good enough to manage issues in the group (A), that your communication and skills are enough to solve problems in the group (B). Also, you must be able to react to events in the group (C) promptly. How can you ensure that? Let's split the answer into three parts.
Part A - environmental specific needs
Where are you diving as a DM? 30°C water, 20m visibility, no currents? Or North pole in the winter? You need to identify the environment to individuate all the variables to put into the group (A), that is, the problems manageable only with skills. If you dive in 30°C water, 20m visibility, no currents, you should be able to manage at least moderate to mild currents (because they can still happen on bad days) and be sure that you do not rely too much on the high visibility, just in case it drops to 10m (it can happen). If you always dive in a lake, clearly you need to manage different conditions.
Part B - environmental experience
As you see from Part A, you must know how to manage worse conditions than the average. How can you ensure that you are ready? You need to test your skills in these dire conditions. That is, gain experience in the worst diveable conditions of your environment. Like it or not, this requires time because you will not experience a lot of bad conditions in just six months.
NOTE: In reality, if you dive in places with highly stable conditions - you can get enough experience very quickly because bad conditions will rarely happen; if they happen, you treat them as part of the group (C): you do not go diving
Even if you dive in places with extremely unstable conditions or change the environment very often, you may gain the experience quickly. But these cases are pretty rare.
Part C - skills and communication experience
Lastly, you need to ensure that your skills, awareness and communication are automatic. That is, you need to:
- experience actual issues (hopefully not serious);
- ensure that your skills/awareness/communications are satisfactory when you respond to the issue;
- if they are not satisfactory, reiterate.
Again, the only way to ensure this is via experience.
In summary, when you have tested your skills, communication and awareness with various issues and in a variety of environmental conditions (that fairly represent the worst scenarios you can face as DM), you may think about going this path.
NOTE: you may be a good DM in some environments, but a very bad one in some "others"; do not lead in the "others"!
I hope people with more experience than me can correct me and improve this answer.
Cheers
EDIT:
1 - I repeatedly used the words "issue(s)", "problem(s)" and similar; what do I mean? Any situation that alters the pleasure of the activity; from very easy issues, like light forms of stress, water in the mask, a double-ender that won't open - to more serious ones, like gas sharing or equipment failures (frankly speaking, I do not wish more serious problem to anyone).
2 - what do I mean when I say "good skills"? Each agency has its own set of standards; when speaking about skills, I like the GUE approach. I believe most people would say that a fundamentals rec-pass level is sufficient for being a DM; you can find the requirement for a rec-pass here, on page 34:
https://www.gue.com/files/Standards_and_Procedures/GUE-Standards-v9.pdf
Is this the best approach to evaluate skills? No; and I don't think there is any best approach