You should not wait to get a new place if you need to accommodate yours and your fiancé’s dog. Once the status on your I-129F changes to, “Case Has Been Transferred To The Department Of State”, give it 3 weeks or so and use their online public inquiry form to request your case number. They likely will not have it available yet but that’s fine because the real purpose will be to give them your new address. After asking for the case number, say something like, “Please also update my address to:”. Give them your new address and also take this opportunity to give them yours and your fiancé’s email addresses as well. This will ensure that the NVC and the embassy has both your email addresses and that you both get all future communications as they will exclusively use email from that point on in most cases.