Agree with all this, except please don’t go to a dog park with unspayed/neutered dogs. It’s against the rules of dog parks in my area for good reason. These dogs get aggressive and are a danger to themselves and others! My dog is neutered but will get interested in female dogs who I guess are in heat. I can think of 2 who have been at the park near us, one a Great Dane who lives next door, and one a very young German shepherd who belongs to some macho guy who I don’t like how he’s training her. The girl dogs don’t like being sniffed like that and lash out. Dog parks are highly dangerous to begin with, and no dogs who aren’t spayed or neutered should be in that mix.
But yeah, you like each other, it’s a hangout, it could lead to a date, why don’t you go on a hike or something.