Claire, I traveled with my kids when they were little by myself frequently. I even took a two-week road trip to visit both sets of parents (mine and my in-laws) with a beach trip in between -- driving 600 miles each way, when my D was 3 and first son was five months and breast-feeding exclusively. It's not that hard.

1) accept that you are traveling at their pace and plan to do it in a way that makes it enjoyable for both of you.
2) little kids don't care that it's elaborate. They want your undivided time and attention. A trip is great for that because it pulls you out of your daily responsibilities. Which is also a great reason for it to just be the two of you.
3) accept that nothing on your trip will be perfect but the memories. She may eat goldfish and ketchup the whole time. It's ok. She can come home to eat lovingly prepared organic veggies. wink eating junk will be part of the adventure.
4) same with sleep. She's getting old enough you can be more flexible about naps. Let go of perfect.

A few weeks before my H moved out I took my kids down to see the cherry blossoms and some monuments. I remember it as a miserable day -- I was so sad knowing we were splitting up, it was incredibly crowded, I worried they'd think it was boring... But as we wrestled through Lincoln, looked at the scaffolding around Washington, and talked about the presidential homes nearby, things we all knew about history (and even my littlest knew a thing or two) and other places we'd like to visit, they thanked me for spending the day with them. And remembered the trip and talked about it at school six months later.

What makes a trip with your child fun? Is it the other adults around you? Or the two of you getting to know each other?

Me42, H40
D12, S8, S7
A revealed: 7/13
Sep 4/14; Agreed to D 1/15

She believed she could, so she did.