I always use lube with insertable toys, so yeah, throw some water-based or silicone-based lube in! That way she can use it immediately after she gets it if she wants to. (Assuming she doesn't already own some lube, if she already has lube then she can probably use what she has.)
I personally wouldn't use lube with a rabbit vibe, but I know a lot of people would. Get the lube. It's one of those things where it's better to have it and not need it, than it is to need it and not have it.
No harm in throwing it in, or you could add a few lubricated condoms to use over it - which might be a good idea either way, since lots of women get bad reactions from jelly toys. The condoms would protect her from that.
I honestly am not sure. I'm not experienced with female sex toys and I want to surprise her.
Here's the link to the product I'm buying. link
Yea, it'd be better to go ahead and get a lubricant because I'm pretty sure most of us women either 1. could not even insert something of that size or 2. would absolutely need lube to assist. So you definitely won't go wrong getting a small tube of lube. Liquid Silk is amazing! So is Wicked Aqua, if you want something thin.