Is it healthy to lose weight this way?

Well, this summer I want to lose about 35 pounds, I actually don't care about the pounds really, I care about inches is all. Im not super walrus fat but im chubby...I have a small frame so I want to get all this ugly fat off my body. Sorry to get off track but anywho...I'll be visiting my mother in the summer for 2 months and she has workout machines that I will be using...such as, a treadmill(: I'm not sure what the others are called but yeah...OKAY sorry anyways...Would it be healthy to eat only fruits and veggies and drink water and healthy drinks? (artichokes,apples,bananas,oranges,brocc… I know it will take hard work but i'm so tired of being chubby, i've been like this my whole life. Right now I believe i'm 5'4 or somewhere around there, and i'm 146.2 lbs. Don't tell me that I don't need to lose weight because even my DOCTOR said i'm overweight. I wanted to lose weight in the first place though but now I have an actual excuse(: Okay Dokayyy....So, yeah incase you didn't get the question...would it be healthy to only eat fruits&veggies&protein for 2 months? and how much weight do you think i would lose? (along with 30 mins. or more of excersize each day)