OP: you've got this!!!!!!!!!
Plenty of single parents and military wives do this all the time, as well as married folk who's spouse doesn't like to travel.
Since my DD12 was 4, we have taken our trips together. We've been to WDW, about 4 cruises, Washington D.C. for a weekend trip via train and Oahu.
I'd love to one day take her to Europe as I went a couple years alone before she was born.
Why do your friends think you are crazy? do they think you should wait to find a 'man" that will help you? or do they play the what if game in their heads? life is too short for all that.
I have 1 friend who was brought up with the notion of you can't do anything without a man and she still thinks it. she thinks women shouldn't be alone in a hotel room

, she isn't ALLOWED-that's right I wrote allowed-to go to her home town by her DF and her DH alone with the kids, only 4 or 5 hour drive, because "something" may happen.
AAA and cell phone plus common sense go a long way.
Even here where we live, she hasn't taken them anywhere, zoo, amusement park unless it's with her husband or a friend, never alone. one time her husband was going to take them to a museum, saw he had to pay for parking and decided against it. ok, that's cheap and mean because the DD knew they were going. but the wife doesn't have what it takes to do things by herself. i hope her husband doesn't die while the kids are young and he is 51 because she won't be able to do anything and that' s pathetic. plus teaching her dd you can't be alone or you have to have someone with you to do stuff.
she is flabbergasted that I have done these things with dd. but our dd's especially need to see that they can do these things when they get older as well. I love to travel even before I had DD, I want to instill in her that love for travel and meeting different people with diverse backgrounds, that can only be a good thing.
and you know what? i think the people who think it's crazy, wish they could do it themselves but don't have the confidence or they could just be party poopers.
have a great time!!!!!!