Transferring care takes lots of patience and preparation but it is possible.
First I would discuss your plans with your current doctors. No one is going to discourage you from going to a place with more support. Ask to get a paper copy of all of your records. You may have to pay a small fee for this service but it's definitely worth it instead of hoping the records get mailed to the correct place. Ask you doctor if he/she has any recommendations for care in the area you are moving to. He may not know a specific doctor but perhaps a good hospital.
Thanks to Obamacare you don't have to worry about having a pre-existing condition and being denied for insurance. I'm not sure if you are planning to apply for medical assistance or purchase private insurance. It's important to know what insurance you will have before you start seeing doctors as you don't want to end up with out of network doctors which will end up costing you a fortune. Or if you know the doctor you want to see, find out what insurance he takes and get that insurance.
As far as your dressing change (I'm not sure if you have an implanted port or a PICC line), if possible, bring someone who can do the dressing change for you with you to your last appointment so that person can learn to do the dressing change. Ask the nurse for some supplies. Either that or coordinate appointments so you can see the new oncologist as soon as possible when your dressing change is due. Most offices that do infusions can quickly do the dressing change for you.
Good Luck and let us know how the move goes or if you have any other questions. If you know where you are moving to, you may want to ask the What-Nexters for advice in your new area.