Hi G.,
My daughter was diagnosed with stage 3 Vesicoureteral reflux on both sides. She was 6 weeks old and got a terrible UTI. It was very scary. She had to have VCUG's every year. Thankfully she outgrew it! They told us she had a very remote chance of outgrowing it because of the severity and the fact that it was on both sides! Her 3 year check, it was gone!
Anyway the VCUG is not fun and at that age can be pretty traumatic. I don't think I'd do it after ONE UTI - especially with a child that age. A baby -definitely, but a toddler can get a uti by rubbing themselves, wiping wrong, holding thier pee too long....
On the other hand, undiagnosed reflux can cause a host of kidney problems. I would talk to your pediatrician, or call down to the urology department at a local children's hospital to ask them if it's truly necessary after ONE uti.
Best wishes to you both.