Hi there, Becky!
Not only is is certainly fine to stay at a Moderate before staying in a Deluxe like the
Beach Club, but Disney makes it easy for you to have multiple Resort experiences in one trip.
Complimentary luggage transfers between Resorts are handled for you by Bell Services; just call the Bell Desk at your home Moderate Resort the night before you are scheduled to transfer to the Beach Club, and the Cast Member will arrange convenient transfer times with you in order to accommodate your requests.
Your dining plan has no impact on where you stay, nor does where you stay have any impact on your dining plan. The only contingencies that would affect your dining plan are changes you make to it: an upgrade, perhaps, or adding on days.
Have a wonderful time in both of your incredible Resorts!
See you later, celebrator,
-Deborah B.