can't export blog. VERY URGENT

Hello,

I have a BIG wordpress website that has 34,000 post & its very important to me to export it ALL to move it to another host.
when every i try to export my DB it stops while downloading & i don’t know what to do about it.
i need to make sure i MOVE it soon before old host expires.. also i wanna make sure all premilinks will be the same cos i got nice results on SEO don’t want to lose them.

I hope you guys can guide me step by step how to fix that to move it safely.

Thank you all