D, I think I understand what you were trying to get at with your OP and yes, someone can be absolutely perfect and yet not know everything.
Let's say I have a two lights, one with a 100 watt bulb and one with a 15 watt bulb. Both lights work "perfectly", meaning that when I turn on the switch they light up. Now, if I were to put the 15 watt light on my front or back porch, it would be horrible because I wouldn't have enough light to see what I need to see. However, if I were to put the 100 watt light on the piano and leave it on all night long, my kids would have trouble sleeping because it would be way too bright in their rooms from the glare of the lamp. I use the different strength bulbs for different jobs, even though both are essentially the same thing, both are light bulbs. Both are perfect bulbs, but the bulb on the porch has a different function than the bulb on the piano.
As with all earthly illustrations regarding God, this one won't be sufficient to truly explain why the Father knows something the Son doesn't know, but as an illustration it should be somewhat illuminating...(ok, bad pun :D ).
The Son is perfect in every way. He perfectly loves the Father, He perfectly loves us, He perfectly kept all the Father's commandments, He perfectly taught us, He gave His perfect life as a substitutionary sacrifice for our sins.
However, in His perfection, He "does not know the day nor the hour". Only the Father knows that.
Does this mean that the Son is not perfect, or more still not God?
No, not at all. This simply illustrates the triune nature of God. The Father, the Son and the Spirit are all One: One in purpose, One in nature, One in identity. But Father, Son and Spirit all have different ways in which God's purposes are accomplished. The Father wills, the Son obeys. The Father knows the "day and the hour", the Son is poised to come when the Father sends Him.
It is not an indication of Jesus' lack of perfection or lack of divinity that even He does not know the day nor the hour. And, rather than give Harold Camping a call, He is willing to wait until the Father sends Him, for that is one of the ways that the Son proves His perfection, His willingness and ability to perfectly obey the Father.
Which in of itself proves He is God, for who would be able to perfectly obey God, but God Himself?
I mean, do you know of anyone who is perfectly willing and able to obey everything God commands of us?