there're two "animal hospitals" just by St Joseph Institution, before the malcom road police post.
i can't remember the names (might one be James Tan Animal Hospital? something like that...), but here're directions from a known landmark:
start at the bus stop opposite Novena Church
go straight along thomson road (towards Ang Mo Kio)
turn left into whitley road (after Thomson Medical Center and the Telecom Building)
keep left the whole way until you see the next exit (look out for smoke stacks/chimneys).
right by the off ramp there's a pet hospital on the right, and another on the left.
my own experience at both places have never been good, so i don't enthusiastically recommend them.
i like the one at clementi, "The Animal Clinic."
Blk 109 Clementi St 11 #01-31
Tel: 67763450
the vets there are always nice. for more choices, you can pick from this website:
http://www.sva.org.sg/en/clinic.php