NO WAY! My daughter is scheduled to have both of those tests you mentioned in February because she has had 13 UTI's in the past 4 years. She has a big history of recurrent infections, and is allergic to sulfa antibiotics which is the go-to to treat these, so we have a hard time getting rid of them without rebounds.
In my opinion, some doctors just love to refer for tests when they're too lazy to try other things first. Make sure your daughter is getting enough fiber in her diet and watch for too much dairy. Constipation is linked to UTI's. If my daughter is constipated, she will inevitably get a UTI. She takes Miralax every other day.
Also, because of your daughter's age, make sure she is wiping front to back thoroughly. Just a little cross contamination of poop to the vagina/urethra can cause one. My daughter is 9 and still has to be extremely careful when she wipes, but don't we all. :)
Good luck and do not think twice about not having that test after one UTI. It's too soon!