Hi @atish,
A warm welcome to the Bunnings Workshop community and thank you for your question.
A good place to start is by checking the manual for the product and then the product's webpage to see if they have any guidance on installing their product in this way. There will often be information on mounting products like this to different surfaces with guidance on the recommended hardware. If there is information on this, it's always best to follow the manufacturer's advice.
It may seem overkill, but as installing an umbrella to the structure introduces lateral forces, particularly from wind, that wasn't factored into the construction of the structure, it would be wise to speak to a builder or engineer for their guidance to ensure it won't negatively affect the structure. It is always better to be safe than sorry.
If the structure is deemed suitable and you are aware of the risk, I'd suggest using the thickest gauge bolts you can fit through the holes in the bracket. Assuming the timber post is 100x100mm, and they will fit through the bracket holes, then some M12 x 150mm Hot Dip Galvanised Hex Head Bolts with an M12 Washer on each side of the post should do the trick.
Let me know what you think and if you have further questions, please don't hesitate to ask.
Jacob
