Please explain to me where I am wrong.

I have a doughnut, a very large massive doughnut made of lead... Ok so it's not edible.

For calculating the force of gravity exerted by this doughnut I can replace it with a point located at its center. Correct? So as I approach this point the force of gravity will increase. As my distance to this point goes to 0, F = G m1 * m2 / r2 will go to infinity. Intuitively this is wrong. Why is this so?