My lo has been to 3 nursery since he turned 9 months. Due to me working in nurseries and moving company and roles. He’s adjusted really well each time. Make sure you are really happy with the new nursery and ask questions around the things you don’t like about the current one to gauge if it’s the right fit for you.
We moved my son after 3 months and he loved the new setting, they also did 7 settling in sessions which was so good for him. Really gentle and he was so happy to spend whole day there after that
I moved my daughter and she settled into her nursery really quickly ☺️
I think the main question to ask, the things you aren't happy with will they be better at another nursery? It will unsettle a child as it's a change but ultimately they'll adjust