Do not trust your gut. You're new to the industry and full of insecurities, doubt, impostor syndrome etc. Many people are. Your gut is telling you all sorts of things that are completely false. Do not trust your gut.

At the end of the day, only you know how you are feeling. If you are not feeling secure about your standing in the company, it's for a reason. Starting your search now gives you the ability to negotiate from a position of power, as you can say no to an offer and wait for another better offer.

Now, WRT trusting your gut... You aren't in a position to know for sure how things will turn out with this company, and you won't know for sure until someone tells you ;) You deserve to be in a place where you feel secure.

If you feel insecure with hardly any reason, you’ll feel insecure anywhere so moving won’t help at all.

OP will probably feel a lot more insecure as the new person at a new company than they do at their existing company where they've already proven themselves and own multiple projects.