She does e-shopping/her shopping.

[dorax]

Is it legitimate to write: 'She uses the internet a lot. She does e-shopping/her shopping.'?

 

[Barque]

She does e-shopping. This is fine.

She does her shopping. This could refer to either regular shopping or e-shopping.

If you mean "She does her shopping on the internet", you have to say it.

 

[dorax]

If you mean "She does her shopping on the internet", you have to say it.

Isn't it clear that it's shopping on the internet since there is the previous sentence: 'She uses the internet a lot.'?

 

[Skrej]

No, because there are many other uses for the internet. It's entirely possible that she uses the internet a lot, but doesn't even buy anything online.

While I'm not bothered by 'does e-shopping', I'd probably still say 'goes e-shopping'.

 

[Barque]

Isn't it clear that it's shopping on the internet since there is the previous sentence: 'She uses the internet a lot.'?

You need a connection to the previous sentence. There's none.

She uses the internet a lot. She does her shopping there/on it.

 

[emsr2d2]

I would use "She [even] shops online".

The standard collocations (in BrE at least) are "online shopping" and "shop online".