I don't think this interpretation is valid.

It seems the dog is suspicious of you, indicating it's not used to strangers coming home with her.

You'd have to be a bit mental to think "oh, that dog looks slightly smug, the dog must have caught every aspect of the social moment and be trying to tip me off".

What's more "girl likes sex, but understands male fragility" - isn't that good a joke. If anything, the fact that the joke requires the audience to see a dog as "tipping them off to slutty behaviour" shows that her read about men being fragile in this area is true and accurate.

When men are litterally joking about dogs wanting to tip us off to a high body count, yeah, that's pretty insecure. So she'd be right to tell a white lie in order to keep the dream alive.