It's never easy to lose a pet. I'm so sorry for you both!
I don't know if you'll see this before telling him the news, but I had a similar situation happen with me. When my hamster died (I'd had her for 2 years), my dad and my brothers were really nice about it. They were very kind to me for the rest of the day and gave me my favorite dessert to help me out a little bit. We had a little funeral for her and everything.
I'd also suggest that you and your son do something to memorialize your beloved pet, like talk about happy memories or things that made you two remember about your parakeet that made you laugh.
If it feels like it's too soon, that's also okay. I just think spending time together when you can would be really helpful for the grieving process. Good luck, and I hope everything turns out okay for the both of you!