There’s nothing wrong with looking for a new position while you’re still employed. It’s the best way to move your career along without taking lots of time out, and it’s a vital step if you’re unhappy in your current place of work.
If you want to start a job search before leaving your current position, though, follow some key rules. It’s crucial to maintain discretion: don’t tell anyone at your workplace that you’re looking for a new job, and don’t search for jobs while you’re at work, or when using work equipment.
Some job websites have an option to hide your resume and profile from your existing employer, and that’s worth using. And if you do apply for a job and land an interview, arrange it for outside of company time if possible, and tell your prospective new employer that you’ve not left your current position. That’ll make the transition easier, and your new employer will appreciate the honesty.