Yes, on Prop Number One, you are allowed to use a bot to copy your own trades from one account to another.
Please note that:
All accounts must be registered in your name (see "What is the Copy Trading rule on Prop Number One?").
Prop Number One assumes no responsibility in case of any malfunction of such bots (e.g., if one or more trades are not copied and/or are closed incorrectly by the bot).