In 1961 the Bubble cut hair style is introduced in the Barbie' world, remember she's got "modern" style to follow...Her skin looks shine and most of the dolls are presented with red lips.The same year Mattel also makes the first red head, called titian. To make sure you get a real vintage 1961 on your hands look for the trademark description on the bottom right-hand side cheek, not found in reproductions.
For more information - vintage dolls: http://fourtyfiftysixty.com/blog/
Picture from: http://dollreference.com/barbie1.html
Picture from: http://www.mybarbiedolls.com/collectible-barbie/barbie-doll-5th-edition-2