I would certainly take it to a major show that had some Error dealers on hand. I am not convinced that it is a Double Die. There is significant evidence of die wear. That can cause mushy strike (Quite obvious on this coin), and other issue like rotational restrike or so on. The doubling on the chin and under the neck is quite pronounced, while the lettering and date have almost no evidence. The thing is, that the further from the center of the coin, the more pronounced the doubling SHOULD be. There are no definitive Double Die errors reported for the 1985 P. It could be machine doubling. There are just too many question marks for me. I would certainly take it somewhere for a second, more expert opinion.