"Whole day" or "all day"?
From the choice you have given
I'm there all day
is correct.
A possible phrase using whole would be
I'm there [for] the whole day
Without the article the your second option doesn't make sense.
Another option is
I'm there for 24hrs
Definitely:
I'm there all day
The other expression is ungrammatical
Whole is almost always used with a preceding article (the/a/an), so something like I ate whole pie is invalid, whereas I ate the whole pie or I ate a whole pie are perfectly valid. The same situation applies to whole day.