We stayed at Claire's with a toddler and baby- the house was well equipped with sleeping options, toys++ and a high chair/splash mat/ long sleeve bibs. The main bed is the best, especially if you end up co-sleeping during the night with little ones. The cot was perfect for our baby too and the curtains shut out the light very well.
For those needing to frequent parks regularly with their kids in tow - St Kilda adventure park (the closest one) is only open certain hours. Jim Duggan Reserve was a playground with soft grounding (good for a crawler) and toddler 10-15min walk away. There are a lot of lovely parks in Melbourne but bark and sand can be tricky at times with a crawling baby.
Kitchen had all we needed for cooking and were able to easily do our washing etc.
We appreciated the extra gifts of books for your children and milk/fruit, thoroughly enjoyed our trip away!