Depending on the grill you own, it may be easily damaged. Some have easily bent legs and weak wheels. The aluminum of many gas grills is somewhat brittle and can break.
If you can, try to disassemble the grill, making notes as required so you can easily reassemble it. If you cannot do this, then try to pack it so that minimal weight is placed on it.
Don't try to ship the propane tank as many carriers will not accept them. Also, clean the grill out so that your other items don't become covered in soot.