The 1st King’s Dragoon Guards badge you show was introduced in 1915, so yes it is correct for WW1.
David Smith has the earlier pattern 1 KDG badge in his website
http://www.britisharmybadges.com/home.php . It’s looped so earlier than WW1 and is very reasonably priced IMO.
The way your 3rd DG badge sits makes it appear to be on loops. If so that would date it’s manufacture to pre WW1 to the Victorian/Edwardian period.
Cheers,
Luke