I do home childcare and have several toddler beds in use..and have used many older ones over the years. Some of mine now have a sort of rail system that they came with. Its really just a rail (that can be removed) that covers the 2 feet or so of space from the headboard to about half way down the bed? Some come off, some don't, but they are made to snap into that specific headboard set up. Most over the years did not have them and I have never had issues with them. Put one side up against a wall...maybe a dresser snug against the other side for that sort of half-rail effect (or a wide toy box or something similar)? In my nap room there is a packNplay turned sideways up against one, so it blocks it a bit in that way for when I start a child out in a toddler bed.
When my own dd (now 16) was the same age as yours, and started in a todd bed, we had a spare crib mattress, so that was on the floor next to her todd bed for about 2 weeks until we were comfortable with the fact that she was not going to tumble out each night (that bed all those years ago had no type of rail)...
Good luck!