I wouldn't worry about resume gaps. I've found that as long as I'm working on some kind of non-trivial personal project (in my case, usually something I have on Github so employers can see it), I can put it on my resume to fill that gap and it's not a problem.
Also, since you still have a job, it's actually the best time to start applying since you can just keep applying and interviewing until you find something while still having a job and receiving a salary. You are clearly unhappy there and are not growing, so there's no reason not to start the process.
Obviously since you're still there you can't just post to LinkedIn saying you're looking (which is how I found my last job, after a more than 6 month gap btw--though I was working on a personal project during that time as mentioned), but you can start reaching out directly to companies.
Even if it takes 6 months to find something, the sooner you start the better.