Traveling around the Taiwan

I want to traveling around the Taiwan next week, I'll use scooter. It's a challenge for me.
I'll travel with my friends, we're all "old ladies".
I think it must be very tired tiring, but it would be very fun.
Because Taiwan is a very beautiful island.
I'll enjoy my traveling.

Almost perfect! 

-"I want to travel" this is future tense. "I am traveling" is present tense.

-"I think it must be very tiring" is correct because it will be tiring whilst you are performing the verb - present tense. You could say "I think it must make you very tired". This is correct because you are talking about after the walked has finished which is the past tense. :)

Traveling around the Taiwan

I want to travel around Taiwan next week. I'll use a scooter. It will be a challenge for me.
I'll travel with my friends, we're all "old ladies".
I think it will be very tiring, but it will be very fun. Since
Taiwan is a very beautiful island, I know I will enjoy traveling.