I don't think it's wrong for council members to vote on officers. That's necessary, as you've noted. But I think it's a conflict of interest to vote for yourself to give yourself more power and authority, which according to the NJ LGEL would seemingly amount to securing "unwarranted privileges or advantages" for oneself.
I'd say let the other council members vote for you if they wish, but I think one should abstain from voting for one's self. I'm not even crazy about nominating oneself, but RONR says it's fine, so nominate yourself if you wish, but I'd say leave the actual voting to others.
To me, it's a conflict of interest issue that Robert's Rules does not address, nor should it. On some level, I like that RONR doesn't get involved in that and puts its focus instead on acknowledging and protecting everyone's right to vote. However, it gets interesting when this position seems to pit Robert's Rules against local government ethics laws, as RONR explicitly permits voting to benefit oneself (i.e. voting for yourself to become "Deputy Mayor", etc.) while the NJ LGEL seems to explicitly prohibit one from voting to benefit oneself.
From NJ's LGEL:
"c. No local government officer or employee shall use or attempt to use his official position to secure unwarranted privileges or advantages for himself or others;" Link to NJ LGEL (PDF)
In this instance (not hypothetical), a certain local government officer used her official position "to secure unwarranted privileges and advantages for herself," in my opinion.
This is simply my current personal opinion on the matter, which may change as more information and understanding comes to light. But I really appreciate your and everyone else's responses on this. They are all excellent and appreciated.
Please pardon my quoting from an older edition. Thank you, Shmuel Gerber, for pointing that out.
Finally, I too am not an attorney, so nothing I post should ever be considered legal advice of any kind. Please seek out the advice of a qualified legal professional if you have any such questions.