Is she aware of the fact that there is no guarantee that it actually is reversible?
It's estimated that the success rate of a vasectomy reversal is: 75% if you have your vasectomy reversed within 3 years. up to 55% after 3 to 8 years. between 40% and 45% after 9 to 14 years.
Information from NHS (national-health service) UK.
So even with the best chances in the first three years, where you would only be 23, you would have a 3 to 1, or 25 percent chance to be infertile, which is pretty high if you ask me, considering your age the fact you denitely want kids in the future.
And what if a condom breaks? First of all if you store and use them corrently that happens pretty rarely. I used them with my ex-partner for 7 years, didn`t happen once and if it still does, I would say the morning after pill would be a way less nuclear option than you getting a vasectomy at 20 years old...