If you do decide to place her in a carrier and take her, they make some really good one especially desinged for dogs. Remember to bring water for your baby too. She will need plenty of that . And protect her from the sun. i'd be concerned for the weather just taking her on hikes .... but, you said the trips were going to be short. I am certain you are going to be very cautious .

I also think your little one, and you are going to feel so much better being together then apart. Especially, that she is your service dog.
Suzi is my service dog too! I understand completely where you are coming from, and know the need to bring my Yorkie where ever I go. It is a necessity .