Welcome to this board 
My ds has a diagnosis of ASD (high functioning end of the spectrum) and has obsessions that can last a good few months (atm it's snails). You have my sympathies...
I assume you've tried redirecting her to something else? Or expanding on the games/drawings etc?
The therapy we use with ds involves a lot of 'extinguishing' certain behaviours, routines, obsessions etc. Much of this means absolutely ignoring 'inappropriate' behaviour (including obsessions) but reinforcing heavily the 'appropriate' behaviour - what you want to see. The theory is that if you respond to a behaviour, you are reinforcing it. If you ignore it, the behaviour fades.
Some of the techniques might work with your dd - eg could try joining in her games with this animal, but only if she chooses a different animal. So she will see that she can have a great time and brilliant game with you, but if she insists on being that same animal, you won't play. So her choice is either play on her own or with you (make sure she understands that playing with you will be much, much more fun for her!), but on your terms, not hers.
Only allow the mask during this game with you. Gradually she might see that the game itself is more fun than wearing the mask, so you can fade out the mask.
When she is pretending to be this animal, totally ignore her. When she talks about the animal, totally ignore it - either talk over her about something else entirely or ignore her and just carry on doing what you're doing. Don't respond to conversation about the animal.
Whenever she's doing something, drawing, games etc that doesn't involve the animal, give her absolutely tons and tons of attention. So she sees she gets more fun, attention, cuddles etc when she's not doing something animal-related.
Hope this makes some sense - it's a bit of a potted and rushed explanation of a specific form of therapy!
Possibly not the right time to say it, but when you're up to it, it is worth trying to get your dh on board. If she does have difficulties which aren't helped they might get worse as she gets older and school/social interaction gets tougher. You don't have to get a formal diagnosis (DH/DPs always reluctant to accept anything "wrong" with their children), but it's about recognising difficulties and helping them, not a 'label'.
Good luck.