This is sorta tricky given the position you're moving to is technically a lower position. A parallel or upward move in that same timeframe would likely be harder, but I cannot imagine it being easy in any case.
Generally speaking, very few jobs allow you to transfer within the organization before 6 months, and those are at private companies that move a little faster than government positions. Furthermore, the first 90 days of your job are absolutely the most crucial--they establish your reputation and credibility. It's rather much like the "first 100 days" of a presidency.
If you do ask for a transfer, it's not necessarily an admission of fault or saying your current position is problematic, unless you already have run into problems doing your job. People move around all the time; signaling that you're more interested in different work is an admission of your aspirations and goals, especially when the position you're asking for is lower paying. Hardly anyone would actively go for a lower paying job unless there was a distinct benefit; in this case, it's your enjoyment of the job.
Concerning being the laughingstock of your department, that should be the least of your worries. Make sure you're happy and satisfied at work and that attitude will rub off contagiously on others, even if your position is reduced.
If they don't give you a transfer, they won't necessarily fire you either. As long as you continue to do good work and you don't bring others around you down, no one will complain. If they do give you a transfer, make sure to wrap up your current work well and hand off things to transition smoothly. Nothing is worse than burning bridges leaving a job, especially if you're staying in the same organization.
Good luck with your decision!

Hi! It depends on the company, but the majority of corporations do not allow transfers before the 90 day probationary period. Good luck!

You have to be happy in the job you are doing in order to do a good job. I would consider it. If you did get it, you could just explain to them the way you explained here. You don't feel comfortable in that position and sought the one you feel you could benefit the agency/company in.

if you want it go an get it make your mind up fast !!