There are more qualified consultants who I'm sure will answer the question, but from a general leaving your job POV which I am more experienced in, here are a few points I would consider.
Firstly, establish whether the issue is your specific company culture or consulting as a whole. Then:
1) If you are looking to leave the industry entirely and permanently, then I would be less concerned about the implications of leaving "too early".
2) If the issue is your company but you would like to stay in consulting, I would change my LinkedIn settings to "open" and continue working while also being open to a move.
I don't think the number of months is too big a concern if you leave for another job. If you leave without another job lined up, I think it may then invite uncomfortable questions at subsequent interviews.
I hope that's helpful, but again look out for expert answers from consultants for industry-specific advice.