Hi rlp,
It's a good thing you're thinking things through. While it's not mainstream for folks to change their jobs right before applying it also isn't uncommon. A lot of time folks line up opportunities that make sense for them and taking them helps the profile. From a recommendation standpoint, if you don't use a current supervisor (because you've only been there a month or so) that's ok and can be explained. However, if you think switching jobs is going to complicate things with your existing supervisor, that'll be a hurdle. It's easy to explain but you'll effectively have no supervisors to bank on.
If the job change is the right decision for you, then I don't think you should let recommendations stop you. But you'll need to mitigate this. As some of the others have pointed out, you can be successful with your apps even if you've just moved jobs.
If you want to chat about this, don't hesitate to reach out to us. We're here to help and I'd be happy to help talk this out with you.
Cheers,
Bhavik