Using an IV is one way to deliver anesthesia, and it does make it easier to monitor the levels while avoiding putting something in their stomach. You don't want them to throw up or refuse to drink something which would make the procedure impossible to complete. There is always some risk in medical or dental procedures, and with anesthesia. I'm not sure that would change if you waited though.
Did you get a 2nd opinion? I see other responses and I'm kind of surprised that so many kids need crowns in baby teeth that will fall out. If the decay is so severe that she will be in serious trouble while waiting for her adult teeth, that's one thing. But if it's not necessary, it makes no sense from a financial or medical perspective. Be sure you are well informed, both on the need for the procedure and the method of administering anesthesia. It sounds like you have a lot of questions that weren't full answered. There's no reason to proceed until you have answers - and sometimes having those explained by another professional can make it clearer. If you see a 2nd dentist, take the original x-rays from the first dentist - they are yours and you paid for them. Usually they will email them but you can also get them on a disk.
Your question should be about IV (intravenous) medication. IVF is something totally different (In Vitro Fertilization - to achieve pregnancy).
Be sure that you understand why your child's teeth are so bad - is there a hereditary factor, or are there dietary or hygiene practices that you should improve going forward so this doesn't happen with other teeth?