Hello M2L
1. Does the quote mean "I'm not ready for it yet?"
— it means 'I'm not capable of doing that at the moment'. You might say it if you were ill, and someone suggested a 20 mile run.
2. Can I say, "I'm really up to that" to mean "I'm ready for it?"
— no; but you can say 'I'm up for that', to mean 'I'm extremely keen on doing that!'
It's more common as a question, though; for instance, someone might say, 'MrQ and I are going for a drink tonight. Are you up for it?' Here, it means 'does that appeal to you too?'
3. Is it a common usage of 'up to sth.'?
Yes; you also have 'to get up to something': either, especially of children, 'to do something mischievous'; or simply 'to do'. For instance, 'What did you get up to at the weekend?'
MrP