Measure distance in astronomical units and time in years, so the constant in Kepler’s 3rd law is 1, i.e
P2=a3. The major axis of the ellipse is 2a=r1+r2 , so the semi-major axis is a=(r1+r2)/2 . Take r1=1 and r2=1.5 per the statement of the problem, then a=1.25 Then a3=P2=1.95 (rounded), so (approximately) P=1.4 . Since this is a one-way trip we divide by 2, getting a travel time of 0.7 years.
Nothing is required except Kepler’s laws and simple algebra and geometry. You do not even need Newton’s law of gravitation.