There are no guarantees but I think you would have a much better shot at finding a whitetail over in the NE corner. There are lots of deer and the regulations are pretty generous with does/any buck for youth hunters.
Have your father call the Spokane Game Dept office at (509) 892-1001 closer to the hunt dates and they can give you a list of landowners that have called in that want some deer killed on their property. These landowners will be helpful (especially for a youth hunter) and point you in the right direction.
Youth General Seasons
White-tailed Deer
Oct. 13-26 Unit 124 Any deer
Oct. 18-21 Units 101, 105, 108, 111, 113 Any deer
Oct. 13-21 Units 127–142, 145, 154, Deer Area 1010, and 172–178 3 pt. min. or antlerless
Oct. 18-21 Units 117, 121 4 pt. min. or antlerless
Nov. 10-19 Deer Area 1050 Any deer
Nov. 10-19 Deer Areas 1060, 1070, and 1080 Anterless only
Next year, be sure to get your license in the spring so you can put in for some special tag youth hunts as well. My boys have drawn three youth doe tags so far and a youth moose tag this year.
Any legal deer is a good deer. Go get 'em!