I am actually the class representative/president for the Masters of Laboratory Animal Sciences Program at Drexel right now.
I did not get in to veterinary school the first time (I only applied to Penn), and so I applied to this program AFTER I heard the decision from Penn, which was not until April. You can usually apply for programs, such as the MLAS program at Drexel, later on. I believe the deadline for the program is not until July 1st of the year you wish to start (July 1st, 2010 for 2010 enrollment). I also know that my roomates from undergrad were able to apply to their masters programs very late (they were applying to medical school).
So my advice for you is to find some alternatives and check the deadlines and then decide... but if you really want to do the Drexel program as your alternative, you are able to apply AFTER you find out about veterinary school. And it is a GREAT alternative, as I am highly prepared for the application this year and feel 10 times more confident. If you want to speak to me specifically about this program, I would be more than happy to talk to you about it and can give you contact information for the program director and any other information you need.
Good luck : )