Children With Level 3 Autism

My family and I are looking to move to the Los Lunas area of New Mexico during the Summer from another State. I have a 3 year old son that was diagnosed with Level 3 Autism last year and just got him established into an ABA facility 3 months ago where he is thriving. Will it be difficult to get him into another facility quickly? Does anybody have a timeline of how the process works? As we know that it is different in every state. Thank you for any and all input.