You wouldn't. You would say "my book or her book", or "my house or her house", etc.
You could use the generic ceann, rather than a specific noun, but it's still possessive adjectives with a noun, rather than possessive pronouns:
"My one or her one?" - Mo cheannsa nó a ceannsa?
Note the use of the emphatic prefix - mo leabharsa nó a leabharsa?, mo theachsa nó a theachsa?