You can definitely see her tabby stripes in the photos. She's lovely.
yes, neutering is definitely recommended and she'll be up and about after the op in no time at all. She'll have a small shaved patch which will grow back in a few weeks. It will help to keep her safe, prevent her from straying in search of a mate when she's in season, will mean you won't have the neighbourhood toms coming round spraying yor property and trying to mate with her, and she's less likely to spray (female cats can do this as well as males).
Cats who aren't neutered can end up having dozens of kittens in their lifetime, often while they aren't even old enough to know how to be a Mother to them, and there are so many unwanted kittens out there - and kittens that grew up without being rehomed, and that people dont want because they're not cute and tiny any more, so definitely go down the neutering route.
I doubt they'll do this just yet, as she's too young right now, but at 5 or 6 months, that'll be when she'll need to be booked in.
She looks so at home under her fake tree.