As of yet, there is no property to get the minimum size of a panel in LabVIEW, but R&D is aware of the demand for this functionality and is currently working on incorporating it into future releases. For now, the only way I know to get the minimum size of a panel is to do so empirically. If you try to set a panel's size below its minimum size, it will return error 1 (invalid input parameter), so starting at a size of (0,0), you can set the panel size over and over, incrementing an axis by one and clearing error 1, until error 1 is not returned. Once it allows you to resize the panel, you can shrink it by one back to its original size and record the minimum panel size. You'll need to carry this out individually for both axes.
I know it's nowhere near ideal, but if you really need to know the minimum panel size, it's the only way I know of. Best of luck!
E. Sulzer
Applications Engineer
National Instruments