In Jainism, every being’s birth and life are shaped by karma. If you want a dog to have a better life in the next birth, the key is to reduce harm and accumulate positive karma (punya) through sincere compassion and right conduct in the present life.

What you can do now, in plain terms:

• Practice ahimsa (non-violence) towards all living beings. Be gentle with your dog; avoid any rough treatment, abuse, or neglect.
• Provide kind care and proper shelter. Feed a humane, vegetarian diet when appropriate, and give clean water, medical care, love, and safety.
• Help animals in need. Support or volunteer at shelters, rescue groups, or adoptions rather than letting animals suffer or be harmed.
• Avoid causing harm to other animals. Keep your dog from harming insects or other creatures, and minimize situations where animals are hurt.
• Practice compassion consistently. Small acts of kindness toward animals and all sentient beings create positive karma.
• Live truthfully and honestly in your dealings with others. Fairness, generosity, and integrity also shape your karmic balance.
• Observe restraint and self-control in your own actions and choices (food, entertainment, and lifestyle) in ways that reduce harm to living beings.

Notes:

• The core Jain idea is that harming living beings creates karmic bondage, while compassionate, non-harmful actions create spiritualle benefits. This applies broadly, including how we treat animals like dogs.
• Digambar and Shvetambar traditions share the same basic view on karma and rebirth for animals, though they may emphasize different scripts or practices in other areas. The essential point for your question remains: reducing harm to animals and cultivating compassion helps improve the future birth for all beings.

If you’d like, I can tailor these suggestions to your situation (e.g., if you’re currently caring for a dog with health issues, or if you’re considering adopting a new animal).