We had a similar problem with my twins when we took them out of their crib when they were about 2 years 3 months. I actually called a sleep consultant, who told me that until they are 3, they don't really have the self control to stay in bed (although my older daughter had done fine when we transitioned her from a crib to a bed... so I guess it depends on the child).
Anyway... we wound up putting a gate at the door of their room. At first, they would scream for a long time. I'd do the whole ferber thing. I'd let them cry 5 minutes, then poke my head out of my room and say "Mama's here, go back to sleep." Then I'd let them cry 10 minutes and come back out again and say "mama's here." then 15 minutes...
What I wound up doing that really helped was to put a big down blanket near the door. That way, when I'd say "go to sleep" I sometimes added "go to sleep on the blanket" and they would just plop down and sleep on the blanket by the door. Worked like a charm.
Of course, you mentioned that your daughter can open the gate. Perhaps buying a gate she can't open would be helfpul. We have one you need to step on. My five year old daughter can open it but our boys cannot (yet). I assume by the time they can open it, I won't really need it anyway... Having a gate up is like making the room one big crib...
Also, if she does get out of the room, just take her gently by the arm and walk her back to the room. Don't talk to her, don't negotiate. She wants to engage you. If you just keep bringing to her room over and over and over (yes, it may take like 30 times), then she'll understand you will not let her be out of the room. The first night or two will be tough, but it will get better when she realizes you mean business.