Will a dog door latch hold better if I stick it higher on the door?

Ha ha, a beagle on a mission! And yes it’s absolutely a force question. I really can’t answer this fully without knowing how the latch is. But I can infer the problem thou. It seems your latch sits right at the door handle.

Which means, the ‘boop’ of her nose is a good enough force for the door. Think of the door as a big lever. The hinges are the pivot and the spot where her nose pushes is the distance from the pivot. So the entire thing acts as a lever mechanism at the door handle. The farther the handle is, the easier it will be to open the door.

Your problem is that the latch sits right next to the handle, right at the door’s edge. Slide it up the door and it’ll still be at the same distance from the hinge line, so it takes about the same pull. The beagle just have to jump higher. Move it up only if that gets it out of her reach. Also I am not sure about the adhesive and the latch itself. You can also try placing the latch in a way that it is not being peeled (like a tape being peeled from the side). If you remount it in a way where the beagle’s push slides along the surface instead of peeling it, it might withstand the load from the boop.

Or if you’re allowed to drill the door, honestly I’d skip the tape and use a latch that screws in. Pups and babies are persistent little engineers in their own way and nothing can stand their determination to open something.