As any experienced parent will attest, Hong Kong and buggies are not a match made in heaven.
Buggies
Stairs are everywhere and trying to find a lift can be very stressful, especially if your Cantonese is not up to much. Many buildings do have lifts but security guards will insist they don't. You'll be expected to lift the buggy up and down stairs.
MTR stations do, theoretically have lifts or ramps. See their guide. However, trying to find the way is often a challenge. If and when you do, you'll have to fight armies of able-bodied passengers too lazy to use the escalators.
Some carriages on the MTR have an area for wheelchairs and/or buggies. Look for the signs on the platform screen doors. They are placed to put you nearest the lifts. Again, you'll often have to jostle with other passengers to secure the space.
Taxis can charge a $5 baggage fee if you put the buggy in the boot, although they generally don't. If you store it in the front passenger seat, it's sometimes easier. Don't expect the driver to help - be pleasantly suprised if s/he does.
Carriers
If your baby is young, you may find a trip outdoors made easy with the help of your favourite carrier/sling.
You'll avoid all the frustration of stairs and baby will like it just fine. In Summer, it can get a bit sweaty, but so can pushing a buggy.
You'll generally be offerred a seat on the MTR/bus, too.
You decide...
Portuguese
Spanish
French