I have learnt that while we study Torah or listening to Torah class online, we connect to HaShem. Are we allowed to have dogs in the room while studying Torah?

Shalom, Thank you for your question. There is no problem with learning Torah in the presence of animals. The only issue would be if there is an unpleasant smell, or if there is animal waste present. May you have every success in your Torah learning and growth, Blessings.