Either:
Wheelbarrow, which is indeed the correct form, means 'a frame or box for carrying a load, supported by a wheel at one end and pushed by a handle at the other'. The word has been in the English language since the fourteenth century. It is formed from wheel, of course, and barrow, a descendant of the Old English word bearwe, which referred to a similar, hand-held device for carrying loads. This Old English word is related to our word bear in the sense 'to carry'.
The form wheelbarrel is an example of a folk etymology. A folk etymology is a modification of a word to associate it with a more common or easily understood word. For example, the word bridegroom was originally something like bridegome, the second element being the Old English word for 'man'. When "gome" fell out of use, "bridegome" was changed to "bridegroom" on the analogy of the common and familiar word "groom," which is at least a plausible substitute.
