I would’t put her down just yet. I have had several hens who have had swollen lower bellies, even for a few years. Some causes can be ascites, internal laying, a hernia, egg yolk peritonitis, or salpingitis. She doesn’t sound like she has EYP yet if she is eating and drinking normally, and not lethargic or lying around. Some of those diseases above may end up causing EYP, but I have had a few big butt hens last a few years. The presence of the enlarged abdomen may “catch” any loose droppings, and they may need to be cleaned off now and then to not attract flies. I would do some reading about the different conditions and just watch her to see how she does. Some use antibiotics early on, such as Baytril to treat any infection if there is salpingitis. You can get it online here or check with a vet:
https://www.backyardchickens.com/threads/baytril-enrofloxacin-sources.959119/
Here is some reading about potential causes:
http://www.regenbiocorps.com/index.php/poultry-diseases/17-disorders-of-reproductive-systems
http://www.theveterinaryexpert.com/backyard-poultry/egg-yolk-peritonitis/
https://www.backyardchickens.com/threads/baytril-enrofloxacin-sources.959119/
Here is some reading about potential causes:
http://www.regenbiocorps.com/index.php/poultry-diseases/17-disorders-of-reproductive-systems
http://www.theveterinaryexpert.com/backyard-poultry/egg-yolk-peritonitis/