Hope some one can answer this. Can "Sophie's up" be uses in place of "Sophie is up". My sister is saying yes and I disagree.

Your sister is right. Sophie's is using the contraction of Sophie is.

I would have to agree 100%; your sister is right!

It may be okay to do it that way, but you should avoid punctuation like this, as well as things like "don't" or "wasn't" in formal papers or other writings. Spell things out for school papers and things like that.