First you have to collect as many reference images as you can for that bird.
Here are some images (even more in google).
Unfortunately I couldn’t find hi-res and more detailed images but that’s a good start.
Note that they aren’t specifically designed for Blender. That does not mean that they do not contain usefull information. Examine them and don’t follow them blindly. Just look for the method of modeling that is suitable for your task.
Third - start modeling. Experiment untill you’re satisfied with the result
Fourth - If you need feedback and help on modeling, don’t be affraid to create a WIP topic here. Your bird will be finished in no time.
Optional - if you’re pressed with time and the budget allows it, buy a ready to use model, or hire someone to model it for you.
Just a note (NO, I’m not trying to freak you out by posting all over your threads, I am just interested in your project), I do NOT recomend buying a bird model that is mass sold, for your logo, you probobly want your logo to be somewhat unique.