Can we pass model as a parameter in RedirectToAction?

Just call the action no need for redirect to action or the new keyword for model.

 [HttpPost]
    public ActionResult FillStudent(Student student1)
    {
        return GetStudent(student1); //this will also work
    }
    public ActionResult GetStudent(Student student)
    {
        return View(student);
    }

Yes you can pass the model that you have shown using

return RedirectToAction("GetStudent", "Student", student1 );

assuming student1 is an instance of Student

which will generate the following url (assuming your using the default routes and the value of student1 are ID=4 and Name="Amit")

.../Student/GetStudent/4?Name=Amit

Internally the RedirectToAction() method builds a RouteValueDictionary by using the .ToString() value of each property in the model. However, binding will only work if all the properties in the model are simple properties and it fails if any properties are complex objects or collections because the method does not use recursion. If for example, Student contained a property List<string> Subjects, then that property would result in a query string value of

....&Subjects=System.Collections.Generic.List'1[System.String]

and binding would fail and that property would be null

Using TempData

Represents a set of data that persists only from one request to the next

[HttpPost]
public ActionResult FillStudent(Student student1)
{
    TempData["student"]= new Student();
    return RedirectToAction("GetStudent","Student");
}

[HttpGet]
public ActionResult GetStudent(Student passedStd)
{
    Student std=(Student)TempData["student"];
    return View();
}

Alternative way Pass the data using Query string

return RedirectToAction("GetStudent","Student", new {Name="John", Class="clsz"});

This will generate a GET Request like Student/GetStudent?Name=John & Class=clsz

Ensure the method you want to redirect to is decorated with [HttpGet] as the above RedirectToAction will issue GET Request with http status code 302 Found (common way of performing url redirect)