Hopefully you have gotten settled but in case you are still looking I would be happy to help - rentals are not very negotiable, unlike a house for sale. Also they go very quick - so I would usually say just look when you are in a month or so range of needing it! Please let me know if I can help with any real estate needs, thanks!
Most rentals do not allow pets but there are a couple that might, what is your budget? There are a ton of houses to buy and you can have dogs, horses, etc - happy to help if you decide to buy! Your monthly payment is considerably lower and you get to make updates/changes that float your boat and build equity! It's historically the best time to buy and I'd love to help you get the keys to your own place anytime you get ready!