Question
About a month ago I noticed a little plant growing in my avocado's pot. I decided to let it grow and see what it became.
Well, my avocado is 6 months old and 12 inches tall. This plant is 1.5 months old and also 12 inches tall.

So it is something that grows extremely fast.

Is it poison oak, posion ivy? I don't think so.

Do you have any idea what it might be? Should I get rid of it?

New leaves
http://a8.sphotos.ak.fbcdn.net/hphotos-ak-snc6/270390_10150240120714263_62062426...

Large leaf
http://a3.sphotos.ak.fbcdn.net/hphotos-ak-ash4/264840_10150240120659263_62062426...

Adult leaf?
http://a4.sphotos.ak.fbcdn.net/hphotos-ak-ash4/267436_10150240120619263_62062426...

Answer
Hi Desirai -
I have family in Birmingham! (Just a shout-out to Alabama...sorry to digress....)
Thank you for sending me the terrific photos. From what I can see, I do not think you have a vine. I think it's a tree. Actually, the leaves look like either an Overcut Oak (Quercus lyrata) or a Sweetgum (Hamamelidaceae Liquidambar). I would try checking images of these trees' leaves online to see if they look like your mystery plant.
Of course, if that thing starts to behave like a vine, I would love to know about it!
Keep me posted, ok?