Looking for a pet-friendly stay in Sydney for a 3-month doctorate placement

Description

I am an equine veterinarian and final year postgraduate student at the University of Queensland undertaking a clinical doctorate. As part of my program, I am undertaking a 3-month placement in Sydney from October until December. I will also be finishing writing my doctorate thesis during this time. My partner Nicholas is a physiotherapist and will be joining me and doing some locum work. We also have a lovely 5-year-old Brittany Spaniel called Baxter, who is well behaved and fully house trained. We are looking for somewhere fully furnished to stay during this period, ideally for the 3 months, but are open to split stays if required. We will have our own car, so the availability of a parking space or street parking is important (happy to pay extra). Our preferred location would be Inner West but we can be flexible.