Since you indicated, in comments, that it's been a month, you should definitely seek another headhunter, if you're determined to do this. I did this for a living for a few years, so this is what my experience was -
The recruiter is going to want to have a happy customer who wants to continue to use his/her services. While they are helping you find a job, which is a huge thing to do, ultimately, the company pays their fees. The company is the customer. You are not. You are the product, and some recruiting firms emphasize looking at candidates strictly as commodities that produce revenue, sadly. Sounds like that's not the case with this recruiter, but the company is still the customer. Placing a candidate who doesn't stick around isn't going to make the client company feel like they are happy.... quite the opposite, so the recruiter is going to either try to discourage you from leaving. They will mention that job hopping doesn't look good, etc, which are valid points, but definitely for their own interests as much as yours. They might want to try and help resolve issues so you stay (as you wondered about in the question). If you're determined to go, you won't find a willing ally.
The recruter who placed you stands to lose their fee, or have to replace for free (my agreements had a three or six month guarantee window, depending on what we negotiated. Had one customer who wanted a one year guarantee, and agreed to pay a higher fee in exchange for that).
The recruiter is almost definitely contractually prohibited from placing you or any other employees of that company elsewhere for some time period (my agreements had a 1 year moratorium for my paid clients).
Your previous headhunter will definitely be reluctant to help, in general, and may be contractually prevented from doing so. So, it may not even come down to you having that choice, but, regardless, you want someone strongly engaged and eager to find you a new position, which would be a different recruiter.
Just be aware, a new recruiter is going to look at you leaving this position with a little bit of "what if this happens with the position I place this person in?", possibly. Be prepared to answer questions that will assure the next person that this was an incredibly unique situation that won't replicate itself, as opposed to a flight of whimsy (from their perspective).
Since you aren't asking about whether it's a good idea or not to leave, and we don't have any information on the exact circumstances, we won't explore those issues.