Hi! The forum here is really enlightening. Maraming salamat sa thread na ito.
Welcome to the forum hungryfortheworld

Regarding your questions...I'll to answer them based on my experiences.
Doctor's fee for a normal check up would cost you around 40RM. That's just the doc's fee and not including the meds yet. Meds are generally cheap and when a doctor prescribes meds during your visit the clinic will usually dispense the meds as well. It's a common practice here since there are very very few, if at all, over the counter drugstores here.
There are many daycare in KL however you might want to take your time searching for the one that suits your standards and budget.
A good daycare would cost you around 500-600RM a month. There are 200RM daycares around but I do not recommend them especially you have a 7 month old baby. They are usually staffed by untrained people whose idea of baby care is to give milk when the baby cries. We tried one of them 200RM daycare once, my baby was around 13 months then and for 2 months she had the worst case of diaper rashes for days that keeps coming back even after doctor's treatments and colds that didnt disappear until we took her out of the daycare. The Chinese run daycares seem to be the best daycares in KL. My advice is to tour the whole daycare and check their facilities before signing up. Regarding stay-out nannies, is it the same as a baby sitter? Sorry, not familiar with the word...lol!
Regarding getting a yaya vs taking your baby to the daycare. If you and your husband dont mind having another person in your house then getting a yaya is the "most convenient and the most cost effective", hands down. The only reason why we havent gotten one is because my wife says she's not ready to share the house with someone else...lol!
Im not sure if you can find a condo for 1500RM near Petronas, CBD kasi kaya prime area. But around KL defintely meron, even cheaper. Cheras would be a good area to look for a place to stay. There are a couple of LRT stations in Cheras and bus ply the route too. We are staying in D'Alamada condo in Cheras, you might want to check it out. Here is their website
http://www.d-alamanda.com.my/concept.asp. I dont think they have a single room/studio type condo here in Malaysia, if they have I haven't seen one yet, but you can find a 2 bedroom condo for less than 1500RM, furnished na yun. There are some property finder websites you can try using to find a condo that would fit your requirements. This is one of them
http://www.iproperty.com.my. You can try using their filtering tool to narrow down your search. There are quite a few postings on the internet regarding property rentals in KL. Try doing a search using google.com.my instead.
If you have more questions, please feel free to post them. We can answer them as best we can

For those members who can recommend any place to stay to hungry please post your resources. Thanks!