Replying to you from the perspective of a librarian, who has been editing materials for 25 years, I would correct it as follows:
"'He disagreed with my suggestion . . .,' she said."
Note that you need opening quotation marks to start your quotation. You need secondary quotation marks to quote the already quoted material and finally, you need a space between the periods used as the ellipses, with the exception of the last one, which is followed immediately by the comma.
This is a basic format, used by Turabian (a baby version of CMS). Other formats are possible -- and they are common, especially in the science fields.
Good luck -- you'll need it. I'd advise you to contact whoever your instructor is, and get his or her preferences for bibliographic notation and usage. Then, stick to what is wanted by the instructor; it can make the difference between a good grade, and a better one!
- For Teachers