wood preserver for bun's playhouse?

I want to paint the playhouse in wood preserver before the trees get all bushy ad I can't get around it. The buns don't have access at all to the exterior so does it have to be pet friendly? I can't afford much at the mo so it needs to be done on the cheap. It's currently a blue colour. Can you suggest anything? thanks

I use a water based one from Wilko i think its called Timbercare and leaves like a waxy/water proof finish. I cant remember how many colours they have, but mine was forest green or evergreen. Wasnt too expensive and i got the playhouse, run and run shelter done and still have a little left over. Theyve taken chunks out of the run and its fine. I think cuprinol do one too, but this ones cheaper.

Search for Cuprinol Timbercare.
Safe for use around plants and animals, that's what we have used on the run and the buns have even pulled bits off it.

Thank you!