OP here. Thank you to all who were kind.
We had one dog come to the birthday party (a very sweet shih tsu named Murphy!), and my daughter had a wonderful birthday.
To the person who was concerned she would get disfigured, I hope this helps you sleep better. I appreciate that your concern probably came from a good place, but I wasn't planning to allow my infant to interact any dog without sufficient adult human precaution exercised on both sides. I promise I'm not an idiot.
To the person who apparently has rage issues about dog poop, I hate to break it to you, but there are absolutely dogs living in 4000 Tunlaw, lol. I'm also not sure why you are on this forum if you have so much vitriol towards dog owners.
If you two need any good yoga recommendations, let me know!