I have sole physical and legal custody. I will be filing a petition for relocation based on NCP moving to Europe and abandoning our child over a year ago, not providing child support, and not visiting. I also will petition to suspend visitation. The NCP appears to have no intention of returning. I cannot afford to support myself and child in our current location with my current income. I plan to move in the US where I have family support, rebuild my career and build savings with a lower cost of living. However, my career path will possibly require me to move other parts of the US.
There is no deadline to relocate unless specified in the order and you must file a petition for any future relocation no matter how near or far the relocation. In practical terms this sounds silly, but you don't want him to petition a sympathetic jurist who may agree that you subsequently relocated without court order.
You should wait to see if the court grants your petition for relocation. You will need to provide the non-custodial parent with notice of your application and they will have the opportunity to oppose the petition. Suspending visitation is another topic altogether. You would presumably need the court's permission to relocate again, in the event that your initial petition is in fact granted. Speak with and retain a family lawyer for additional information and in advance of filing documents with the court.
First off, let me say that you have a very strong case for relocation and, if everything you stated is accurate, the Court will allow you to relocate.
Once that is granted, if the non-custodial parent ("NCP") continues to be completely absent (no visitation), then you can move whenever you want. But, if the NCP starts to have regular visitation and you do not move for a long time (> 6 months), you could have problems in trying to relocate after that if one of the reasons that court granted the relocation was because of the NCP's lack of contact with the child.
You need to consult a lawyer on this issue.
I do not agree with the attorneys on this post. If the facts are as you explain. I would simply move as there has been no contact for a year. If he were to file here complaining about your move, which I doubt he will, you can always deal with it then because, if you establish residence elsewhere, there are exceptions to the law regarding jurisdiction of the case which would clearly justify jurisdiction in the local Court in the state in which you set up residence.