Agreed, it's kind of cool!
Pigeon are game birds and have higher amino acid requirement than chickens.. and if your feed is "layer" then it will have excess calcium for a non laying bird.. IF that's all it had to eat.
BUT.. free ranging, not knowing the age or gender of the bird, or how long it will stay...
Truly.. Brahma are a dual purpose hen.. and will do *best* with at least 18% protein. You might consider switching to an all flock feed.. Purina Flock raiser is 20% protein.. and higher in amino acids... 16% of most "layer" feed is the bare minimum to keep a light bodied layer like leghorn in good condition. Since making the switch and providing oyster shell free choice on the side.. my birds have less harsh molts retaining their full personalities and returning to lay sooner. I have used it for raising.. ducklings, chicks, hens, roosters, etc. Please note that it gives more budge room for treats if that's your thing as many are low protein. The extra nutrient also offers added immune system support..
Usually game birds (quail, turkey, and pigeon I think) also require much higher protein when young.. 24-30% depending on species and age.
I would be sure and check my birds at night time once monthly... and that bird if you can get your hands on it after dark while they're tucked on roost.. and look for lice (etc).. parting feathers below the vent and on abdomen look for crawlie things running away from the light. Keep it dim to keep the birds calm and use a flashlight for this process.
Birds are so fascinating!
ETA: maybe there are other ways to add Omega's to the hens diet if that's a key element for ya??
