Why on earth does the father need to "prove" himself to the op? He has a relationship already with his daughter where he sees her regularly and presumably enjoys that time together. He is just as valid as a parent as the op,what on earth makes you think he shouldn't give his daughter the chance of a lifetime??
I bet any money you like that if the op had come on saying she was taking a loan out from her local credit union to go on a holiday to Australia with her dd everyone would be wishing her well.
How is it odd that he takes out a loan with HIS money and DOESN'T ask op first? It's his personal finances, none of the op's business where he gets the money from to pay for the holiday.
Also, with a credit union you have to have at least half the loan amount in savings with the union first. He hardly sounds financially irresponsible if he is managing to save regularly. The loan would be paid off by the time he goes, it's no different to me booking a holiday now, paying the deposit and then paying the installments to clear the balance by the time we go on holiday.