Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If your job involves handling and touching dogs and cats, then some of the strict laws of taharah or ritual purification are not applicable to you as ruled by Imam Ibn Taymiyyah and others.
Answering your question, Sheikh Ahmad Kutty, a Senior Lecturer and an Islamic Scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Islam teaches mercy and kindness towards all of God’s creation, including cats and dogs.
In other words, while you should do your best to wash with soap and water all those areas you come into contact with urine, droppings, and saliva of dogs. You are excused of what you cannot.
Therefore, the fact you are handling dogs should not prevent you from performing your prayers on time. You should pray by doing the best you can in the given circumstances. Allah assures us in the Qur’an that He does not punish us for things we have no control over.
It is important for me to point out: while the majority of scholars say that dog’s saliva is najas and we should wash our clothes or parts of our bodies if we come in contact with it. However, Imam Malik does not share this view.
In conclusion, I would urge you to pray on time and not to put off your prayers until you get home.
Allah Almighty knows best.