Parent buying Minecraft (Windows 10) for child

You can buy games as gifts. During your purchase, you can enter the email address or 'gamertag' of the recipient, and after the payment, they will receive a link to accept the game and add it to their account.

In your case, it's easier to initially set up your child's account on Windows 10 through your own account, after which you can set parental control on theirs, and more easily buy them products. If they already have an account, you're going to need access to it to set the parental control.
Here's a guide to do so - I copied the instructions verbatim:

• Open Windows settings and select 'Accounts'.
• Select 'Family & Other People' from the left-hand menu.
• Click on 'Add a Family Member'.
• Select 'Add a Child'.
• Enter the email address of their Microsoft Account below if you have it.
• If your child already has a Microsoft account, click through the remainder of this dialogue. If not, click 'The person I want to add doesn’t have an email address', and set up a new Microsoft account.
• After this, you can start adjusting the child's account limitations to your liking.

You may have an easier time buying the Java Edition and creating an account there. Your question wasn't too clear on whether or not you two share a laptop or necessarily want to share an account, but in either case it's pretty simple to make an account for both of you here.

In this case you create a Mojang account and it's completely independent of a Microsoft account (as your comments mentioned you'd like to avoid).

This takes Microsoft out of the equation entirely but it doesn't allow for you to create a "child" account necessarily or create parental controls. But in this case you just set up an account and you're ready to roll.

Plus the Java edition has the added bonus of much more customization compared to the Windows edition (which charges for things you can get and do for free in the Java edition).

I set up something like this for my nephew.

First, create an account for yourself.

Then, create an account with parental controls for your kid with yourself as the guardian.

Your kid can use this account to log in to Minecraft Bedrock regardless of device (so they can use the pc, but for example, my nephew uses tablet, I use mobile and XBox One and they're all compatible with eachother) but will not be able to join multiplayer servers or realms unless you give them permission to do so.

Not sure of you would need to buy the game for your kid, or in their name, or just buy it on the computer you'll be using it on.

Edit: I was going to expand these instructions, but you can just follow Joachim's answer for fuller instructions.

If you buy the full game from the store, your child should also be able to play it when logged in to the laptop with his profile.

I'd recommend you register a Windows account for yourself and your child, and then setup a family profile. With this you will have easy control over how long he can play etc. You'll also need to setup an XBox Gamer profile with the same account. It's all fairly straighforward.

The Windows version is very nicely integrated with the whole XBox ecosystem. I believe the Windows 10 Minecraft license will also cover the XBox console, if you ever get one of those.