Williams, 17, spent his entire youth career with Doncaster and has been training regularly with the South Yorkshire outfit's First Team since the summer of 2024.
The highly-rated youngster made his first steps into senior men's football with the Seasiders when he made his debut at Bamber Bridge in January's 2-0 win at the SFC Stadium.
Whitby Town manager Gary Liddle said: "I'm pleased Kasper has extended his loan with us. He's proved that although young in age, he has the right qualities and attributes to help us further.
"I would like to thank Doncaster Rovers for their help with the deal to start what I hope can be a good relationship between both clubs for the future."