Try delcies, they have eggless cakes. Then buy cake toppers/decorative items (I've seen some cartoon design ones) and cute candles from qoo10 or taobao. http://delcies.com
I want to recommend delcies too. They have eggless cakes n you can customise them. Otherwise emicakes also have eggless cakes
You can try Yes Natural bakery located at Aljunied MRT. http://www.yesnatural.sg/page-fnb-bakery/
Emicakes have eggless cake but for the pony design I'm not sure but their cake are delicious
U can try checking FB for nanabake https://www.facebook.com/nanabakecakes/