The link I provided before will help you to understand most of the requirements.
Here's the link again:-
https://www.gov.uk/join-family-in-uk/overview

Yes that is the UKVI webpage for those people wanting to 'Apply to join family living permanently in the UK'
So that webpage applies to both you and your child.

If you look under item 6 'Apply' you'll see that from the Philippines the application is made online.
So you'll be 'filling out' the form online. As you work through the form there'll be a number of options to select via drop-down-menus and you'll need to select the option that applies to you.
So you'll be able to select the correct Visa Type for you and your child once you have completed the previous Mandatory Online fields.

The specific Visa Type will of course depend on your marital status at the time of application.
But in principle

You and your child will each need an application. You'll be the one to complete the application for your child.

If you'd like to make some practice runs and get a feel for the online application and various drop-down menus
then follow this link

https://www.visa4uk.fco.gov.uk/

In the menu for select visa type the reason for visa will be 'settlement'
Type of visa will be 'settlement'
The Visa Sub-Type menus will then be displayed and you'll see a visa sub-type as 'unmarried partner' (unless you are married at that time in which case select wife)
You'll see there is a sub type for child as well/

I'm sure it'll all become clear the more you use it.

Hope that helps at this stage