Just say no to WD-40 unless it's sticking. WD-40 is designed to free up stuck parts & displace water allowing lube to get to the surfaces in contact. There's only a bit of mineral oil in it. The oil mentioned in the first reply was likely 3in1 oil or something like it. Very good choice. Oil, use, oil again after using for a few times to clear out the corrosion. Spray lithium grease is good but will be hard to get to coat the whole shaft.
That said depending on the wheelbarrow there may be a grease (zerk) fitting which you can pump grease into, which is the best way to lubricate the shaft & bearing, & the absolute most satisfying. Watching the grease ooze out of the wheel hub & the squeek going away is sooooo, nice.