a dot instead what ?
can you be more explicit?

you juste want an empty badge ?

<q-btn push color="white" text-color="primary" label="Unread Mails"> <q-badge color="orange" floating>&nbsp;</q-badge> </q-btn>

you want a exclamation ?

<q-btn push color="white" text-color="primary" label="Unread Mails"> <q-badge color="orange" floating>!</q-badge> </q-btn>

you want an icon ?

<q-btn push color="white" text-color="primary" label="Unread Mails"> <q-badge color="orange" floating><q-icon name="warning" /></q-badge> </q-btn>