As the parakeet is missing the late budgie, I would definitely get a new one, but keep it in its own cage, until you see if the two birds get on.
Unless, of course, you feel that looking after two birds is too much work for you now. The parakeet will get over the loss, but I have no idea how soon that will happen.
My tom cat looked at the empty sofa yesterday, as if to say, "Master should be sitting there." It is now nearly a year and a half since my husband died, and I honestly thought both cats had stopped missing him, but apparently not.
On the other hand, when the first of our previous pair of cats died, it only took nine weeks before his brother resumed hunting mice in the garden, and growling at dogs walking past the garden fence - he had apparently not felt either activity suitable while he was mourning his brother.