Is the topology in this image good for animation. And can I move on to professional level with this kind of modeling
You should avoid tris and ngons in your geometry, even if its a game model (its ok for mobile game models though - depends on polycount)
The meshflow is ok, its not good around the nostrils. Here is a good edgeflow that I recommend, its from a Zbrush course:
You will know when you are ready for professional level, someone will just employ you. There are different levels among professionals too. Just practice and your confidence level will increase. You are basically ready when you know what you are doing.