The reputation points you see in the pop-up after donating animals increase your standing (member rank) in the club - this can be seen with the little icons that appear next to your name:
Rank 1: Small Bunny is your base rank.
Rank 2: Clever Fox is unlocked at 500 reputation points.
Rank 3: Mischievous Monkey is unlocked at 1500 reputation points.
Rank 4: Mighty Bear is unlocked at 3000 reputation points.
Rank 5: Proud Lion is unlocked at 5500 reputation points.
These ranks are just cosmetic, and let the rest of your club now that you're an active contributor to the club.
The points that go towards the contest are calculated differently: You get 10 points (* animal level) per donated animal. So regardless of whether you donate a level 1 rabbit or a level 1 horse, you will get 10 points per animal. If you donate a level 3 animal (that you bred), you will get 30 points.
Additionally, the top three donors get a multiplier on their donations. The player with the most donated animals gets their score multiplied by four; the second highest gets their points multiplied by three; the third highest gets their points multiplied by two.