Elronds parents

[Guinevere]

This quote from one of Tolkien's letters (explaining elvish names) suggests that Elros and Elrond really were still toddlers when left by their mother:

Originally Posted by Tolkien,letter211

*rossē meant 'dew, spray (of fall or fountain)'. Elrond and Elros, children of Eärendil (sea-lover) and Elwing (Elf-foam), were so called, because they were carried off by the sons of Fëanor, in the last act of the feud between the high-elven houses of the Noldorin princes concerning the Silmarils; the Silmaril rescued from Morgoth by Beren and Lúthien, and given to King Thingol Lúthien's father, had descended to Elwing dtr. of Dior, son of Lúthien. The infants were not slain, but left like 'babes in the wood', in a cave with a fall of water over the entrance. There they were found: Elrond within the cave, and Elros dabbling in the water.