To address Torben's comments...The power supply only needs to deliver a peak of about 31 mW (9mA) assuming a transmitter efficiency of 20% which is a rough guess for these power levels. If it is pulsed on and off, perhaps it would average out to 15 mW or less. 3.5 volts is plenty for modern ICs to synthesize the carrier and boost it out at 8 dBm since this is a common voltage used in cellphones and other stuff. With a NiMH battery from a small cellphone, we might expect 700 mAH, which translates to about 155 hours of continuous pulsing. That's reasonable for a start. It wouldn't be too tough to reduce the duty cycle and extend the battery life, to some degree.
The "in the city" thing is a tough call, because the shadowing and multipath causes a lot of variation of signal as the bird flies around. But you have the benefit of the human brain listening to the signal, and it is very adaptable to losses of signal and the ups and downs of SNR so it might be frustrating in the city but it might also work some of the time. This also helps to deal with those problems I mentioned of polarization mismatch and the lack of an omnidirectional pattern from the bird. The human being will just have to cope with signal going in and out of the noise floor over time spans of several seconds to tens of seconds. But humans are adaptable, as many of these threads demonstrate.