Clintasha from the beginning

Hey so this story isn't based on the real story of how Clint and Natasha met, i'm just making my own thing up but there is going to be The Red Room and S.H.I.E.L.D but i'm just going to tell it way different of how they met.
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when Clint has finished his mission he returns to New York, he has gotten the day off for good work and he got threatened he would have to teach the newbies in S.H.I.E.L.D, that was enough for him to have a day off. On his day off Clint took his dog Lucky for a jog in the park that's not far from S.H.I.E.L.D so he could still keep a close eye on the building, while he was jogging his dog ran off and he wouldn't come back when he called so he ran after him and saw him jump on some woman.

Natasha was currently spying on S.H.I.E.L.D she was told just to see what they do and to return back to Russia, she was in the park for her last day before going back, her cover was a girl out walking her dog, she was borrowing someones dog saying she was hers, she had stopped to let the dog off the lead and to take some notes, just as she was finishing, a Golden Labrador appeared out of nowhere and jumped on her.