How long ago did you get these new chickens?
Separating her will certainly keep the other chickens from picking on her.
Being alone is stressful for chickens, but so is being picked on, so I don't know which is better in that respect.
If those chickens have been together for a few days, they are already exposed to each others' diseases, so separating her now won't make any difference to that. But if you just got them today, then they might not have traded all their germs yet, so separating her from the others might still help.
If it was me, I would probaby put her in the dog crate, but put the dog crate inside the pen with the other new chickens. That way she is safe, but not entirely alone.