I take my girl with me as much as I could. So I got several suggestions
there are carriers that you can strap to yourself, strollers, purse carriers or even "purse" harness (where you can carry them like a purse). There's also car-seats/boosters. I have everything, myself, and am awaiting a stroller I just bought. I also find out about places that are pet friendly or don't mind pets. Aside from pet stores, I've found craft stores such as Hobby Lobby and Michael's are pet friendly. I think home depot is too but I do know that Lowe's stopped allowing pets. I remember seeing a list on pinterest on pet friendly places, but it's still advised to call ahead of time and be sure if they'll allow it as some specific store's management may not allow it. Also there's parks and stuff. I'd check the local areas for such places. Any place that serves/sells food will not allow pets and I know that service fields that are personal, like spas and salons, don't allow pets because of sanitation reasons, as well.
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R.I.P. Mick & Mandy (before 2010), Mila - 4/3/15, Chloe - 2/18/16, Kimchi - 6/2/2021