I figured on the timeframe b/c the 3 credit reporting agencies have 30 days to respond to your letter and make a determination, ask you for more documentation, etc. Once your dad's black mark on your credit is gone I also figured on some time needed to get the score changed, though I may also be wrong there, it could very well be instant.
Personally I wouldn't bother shopping for a loan until your credit report is correct. Sure, you could find someone to make the loan but it's not likely to be at the interest rate you want.