Hi Emma, Hollie sounds like such a delightful little girl!
I think if you are happiest at home, she's not missing out on anything. At three months, Natalie was easily overstimulated and seemed happiest at home. I took her out with me a bit though, but that was because I wanted to get out - not for her sake. Its really up to you. I've discovered that a walk around the garden introduces a whole lot of new sensations - that's an easy, hopefully not stressful way to get out if you're looking for one
As for leaving her for a few minutes, I think there's absolutely nothing wrong with that. If Hollie is happy to play on her own for a little while, that is great. Natalie used to last about 15-20 mins too before starting to get bored, tired or whatever. Use the time for yourself and don't feel bad about it - you deserve it! And its probably good for Hollie's development to do things on her own a bit. How good are those baby gyms?! Natalie loved the gym too... still does at times