The test for iron is a blood test, but it's generally a simply finger or heel stick. Nurse through it or right after it and the baby is unlikely to mind much. It's going to hurt you more than him. If you had low iron during pregnancy and baby was low birth weight, IMO you definitely want the test done, even though you are taking a multivitamin. The iron in breastmilk is generally sufficient for the baby's needs, but some breastfed babies do become anemic even when mom's iron status is normal.
Olive oil on fruit does sound yucky to me, but I would try it anyway. Your baby may not have the same palate as a grown-up!