As of right now, no--because you do not have the money and did not follow the process for obtaining the pet. Staff are human and they will be able to sort through it/correct it. They are very understanding and several of them have been at this for years.

You can get a rabbit when you have the money for it (9 galleons) and complete the application process (as outlined/explained in the first post of the Pets thread).

I recommend you to join the mentorship program @Rowena Nightshade! It's very helpful, I joined too -- it's great for new users! Also, welcome to the site and to Hufflepuff!