Hi Tiffani,
Disney's Beach Club Villas are a wonderful place to stay. I love the quaint feel, and the walking distance to Epcot is great!
I am going to suggest to you that when you are heading from Disney's Beach Club Villas to Magic Kingdom that you take the bus. I think that it will be more efficient for you. The bus ride should be around 20 - 30 minutes of driving time. You also need to factor in that you might wait a while for a bus, at most probably 20 minutes. So I would allow yourself 40 - 50 minutes by bus, knowing that this may be an overestimate.
There are a few issues with taking the monorail from Disney's Beach Club to Magic Kingdom. First of all, while you can walk to Epcot from Disney's Beach Club Villas, you will enter through the International Gateway, which is in the World Showcase area of Epcot. From there, you will need to walk through World Showcase and through Future World to get to the front of the park, where you catch the monorail. You need park admission to get through Epcot. If you have base tickets, this option will not work because you need to enter two parks that day. My guess is that this walk will take you 20 - 30 minutes to get to the front of Epcot. You will need to take two monorails to get to Magic Kingdom. From Epcot, you must first go to the Transportation and Ticket Center, where you will switch monorails and catch one heading to Magic Kingdom. I think this will take you about 30 -40 minutes when you factor in wait time for each monorail. My estimate on this - again possibly an overestimate - is 50 - 70 minutes. Also, you will be more tired when you reach the Magic Kingdom from your walk through Epcot!
I hope this helps, Tiffani, and please do visit us again if you have any further questions about planning your trip. We on the Disney Parks Moms Panel love helping you to plan magical vacations!