Is it better to get my passport renewed before applying for an H4?
Once a Visa is issued and a sticker pasted, it remains in the same passport which you have to carry while travelling alongwith any subsequent passports issued. You may get your H4 stamping sooner than a month or almost in 23 days if approved instantly. More than one year of validity of PP is a way too long to go. Six months validity is insisted before applying for H4 and is also a requirement by Airlines to enter into the Country. Even if you plan to differ your travel dates after the Visa is issued, you still have more than six months time and a choice to apply for a new Passport.