First off, feel free to start interviewing now. Most places have a 1-2 month lag time between initial contact and the day you start the job.
Second, don't feel obligated to take the first job offer you get unless you're ok with drifting from job to job like some people are. It's better to have some focus about your career and doing what you enjoy. If they offer and you honestly don't think it's a good fit keep looking.