In my opinion it would be best to keep your new girl on lead and muzzled at all times.
You should keep her on lead unless you can find somewhere that is totally enclosed and you can let her have a run about. That way she is safe and you are relaxed that she cannot hurt herself or take off after something that she has seen.
Every dog is different and you will get to know your new girl best, but it is much better to have a dog on lead and safe and happy, than one that injures itself or another pet. That would be very upsetting for all concerned. And would not be a very good advert for rescue greyhounds.
My Reo has been with me for 11 months and has only been off lead a handful of times in a totally enclosed area. He is safe and happy and contented and I am confident that he will not come to any harm, nor will any other small furry animal. Although he is a big docile lump of a boy, I never take any chances around small fluffy dogs. I do not want him to get hurt or him to hurt any other dog or cat. I am always aware that Reo and I are flying the flag for rescue greyhounds, who in my opinion are the best dogs in the world. I think that’s official!!
Reo is at present away for a few days with his dad and his sister Amber. I was unable to go due to the gala. I am missing the dogs now that the baking and sandwiches are all done. They will be back possibly tomorrow and I look forward to seeing the big fella and of course the Diva!
Hope this helps and again lots of luck.
Remember we want lots of stories about her progress.
Joyce