This will be my first time traveling out of the country. We will have a layover of 45 mins in Fort Lauderdale before departing to Cancun. Will we have to go through security again in Fort Lauderdale or just get onto our next flight?
This airport doesn't have an airside pedestrian access, nor airside buses or trams. All transfers between terminals are accomplished by exiting the terminal and taking shuttle buses that run regularly around the airport from one terminal to the next.
Assuming your first flight has departure from a US airport, whether you'll go through security again at Ft. Lauderdale will depend on what airline(s) you're on, and whether your flights arrive and depart from the same Ft. Lauderdale airport terminal. If you edit your question to provide airline and flight information, a more specific answer can be provided.
TL;DR: If you have to change terminals in Ft. Lauderdale to reach your ongoing flight to Cancun, you'll exit the arriving flight's terminal, shuttle to the departing flight's terminal, then have to go through security again to reach the departing flight.
FLL is in the process of building airside corridors between its four terminals. However, at this time only one of them is complete, that between T3 and T4. The rest are expected to be completed by 2022.
If you stay in the same terminal, or if you are going between T3 and T4, you won't have to clear security again (unless you arrive on an international flight; you always have to go through security again after customs to change planes in this case). Otherwise, you will need to go outside to change terminals using the free shuttle that runs between all four terminals.