Snopes says it's fake.
1.) I do not believe the Queen is going to carry anyone's golf clubs, nor do I believe she is currently healthy enough to do so if she , for some bizarre reason, decided to.
2.) I also do not believe President Trump would expect her to do this, or allow it under any circumstance. He'd carry his own, or assign it to some fit young assistant.
A minor note: They're not on a golf course. That should be a .... "clue."