HI Jackie,
As far as Penn Foster is concerned - if the clinic you work at meets all the requirements, you can do your Veterinary Assistant Externship there.
It would be up to you and your employer to decide if your externship skills can be done on your paid work time, or if you would need to come in on your time off. Sometimes this arrangement will depend upon your position at the clinic - see meg825's example. Sometimes this arrangement will depend on the clinic's policies - some clinics will not allow employees to complete school required externship tasks during their paid work time; other clinics will allow it. We leave that arrangement between you and your boss.
I hope this helps!
Dr. Amanda