The orbital period of a planet depends on both the radius of the orbit, and the mass of the star, and the range of habitable radii depends on the luminosity of the star, which depend on its mass and age.

Also, you only needed the third law. Assume the orbits have approximately the same eccentricity, and the semimajor axes will be proportional to the mean distances. If your planet is 1.3 times as far from its primary as Earth is from Sol, and it also has an approximately circular orbit, then the semimajor axis is 1.3 times that of Earth's. In fact the semi-major axis of a near-circular orbit, is pretty close to the mean distance from the primary.

The planet is going to receive less energy that far out, so you need to make the star brighter to keep the planet from freezing, you need to raise the luminosity by the square of the change in radius to do so. So the star needs to have a luminosity 2.2 times that of Sol. If it's the same age as Sol (4.7 Ga), I think you would need an F9 class star (I'm working backwards using the star system design rules in GURPS Space at this point) which would have a mass of 1.15 solar masses.

The square of the orbital period is inversely proportional to the cube of the mass of the primary, so doing all the math: (1.297^3/1.15^3)^(1/2)=1.198, Multiply by 365.25, and we get 437.5 earth days.

I'm open to being corrected by anyone who actually knows something about Astrophysics though.