I would probably keep any pets out of sleeping areas. There is an association between exposure to cats and dogs and lower rates of asthma, in the sense that people who have cats and dogs in their homes as babies tend to be less likely have asthma, probably because there is something about being exposed to those allergens that is protective for the immune system later in life. But cats and dogs don't have bedding and I would imagine that kicks up more dust. I wouldn't feel comfortable with that where my baby is sleeping. I'd think of it as a risk in the similar way to other airborne pollutants, which can sometimes increase risk of cot death. Apart from the health issues, which may have more to do just with the health of your baby and the health of your bird (if you've had him/her vetted and checked for any infections, etc.), while it might work for a few months (if you have a baby that is an amazing sleeper, not one that's woken by every little noise), once he/she becomes mobile, it will be like having a toy in the room that can be poked, have things thrown at it, and something to try to play with instead of going to sleep. Health issues aside and I would ask a doctor about that, but I think it would just make sleep really unnecessarily difficult. I would imagine all that would be stressful for a bird, not to mention, the many wake-ups and crying throughout the night.
Is it possible to put your bird in your main living space and up away from poking hands? Or you said, you had 2 bedrooms, is that den one of those bedrooms, or are you saying you have 2 bedrooms plus the den? If so, obviously, make use of that space for both baby and bird. That would make more sense to me. Or if that's not a possibility, would you consider re-homing your bird? In the absence of enough space for everyone, that would be your only other option unless you can get a bigger house.
