I was wrong in thinking that you can't add the latest news block to My Moodle. It is possible to show the site news in the latest news block.
Hellen, I just tried in 1.9 and found the same as you. It seems there is a bug. Please report it in the Moodle Tracker. (You'll need to create a tracker account in order to report a bug.)
Kristbjörg, in Moodle 2 you can show the site news on My Moodle by logging in as an admin, browsing to Site administration > Appearance > Default My Moodle page and adding the latest news block. You then need to edit the block and set "Users My home page" as the page type and "Any page matching the above" as specific sub-page.