Ah, prepositions and phrasal verbs... They must be so fun for learners. To complicate matters, and perhaps this a feature of British English, but the question 'are you up to it?' has an additional meaning. It means 'are you capable of doing it?'
Example situation. Someone has to give an important presentation but has been feeling unwell in the days leading up to it. Their boss might say to them:
It's important this presentation goes well. Do you feel up to it or should someone else step in?
It means 'do you feel that you are able to give the presentation' in this situation? More generally, do you feel able or capable of doing something?