Go on https://hiu.state.gov/data/data.aspx?view=table&sort=title+asc
Download 
- Detailed World Polygons (LSIB) - Americas - March 2013
- Detailed World Polygons (LSIB) - Eurasia/Africa - March 2013
Unzip Data

Get Capital Cities
Download dataset coming from here http://www.arcgis.com/home/item.html?id=dfab3b294ab24961899b2a98e9e8cd3d
Load into QGIS
Filter out cities with attribute STATUS=National and provincial capital
Save