A fun approach. Something to consider for a different (probably more complicated) approach:
Start with 10 'guessing points'
Make buying a letter cost 1 point.
Make buying a random square (1 out of 16 for instance) of the picture cost 1 point.
Make buying a hint cost 1 point.
If it is guessed (typed correctly) before 10 points: Bonus points. If it didn't happen: Negative score for that one.
Other than that, I'd like the letters to all be present, for instance: D E E R (instead of D E R) for deer.
The selection shows the number of the animal when hovering over the squares with question marks in my browser, this might give people a small advantage (who knows, maybe this will be played at top level someday).