How long after a 2 y/o beagle has had puppies can she become pregnant again?

Why do you want to know?

My beagle had a litter on April 7th and looks as though she's going into heat again. I need to know if I should pen her up or not.

Personally I would get her spayed. That's the only way to make certain she doesn't have another litter.

Good luck.

Yes, pen her up. For her own health please consider spaying her and do not continue to breed her.