강아지가 귀엽다 is possible

For 는 or 가, Refer to https://www.italki.com/question/429082

-ㅂ니다 and -습니다 are the ending suffix of Hasipsio-che
-ㅂ니다 is used after a verb or adjective which ends with vowel or ㄹ
-습니다 is used after a verb or adjective which ends with consonant except ㄹ

-다 is the ending suffix of Haera-che

-(어/아/여)요 and -에요 are the ending suffix Haeyo-che

Hasipsio-che(Formality: high, Politeness: high)
is a common style of speaking. A conversation with a stranger will generally start out in this style and gradually fade into more and more frequent haeyo-che. It is used
between strangers at the start of a conversation
among male co-workers
by TV announcers
to customers

Haeyo-che(Formality: low, Politeness :high) is remarkable in that it is used both with higher level pronouns (namely, titles) as well as the middle level second person pronoun dangsin. It is used mainly:
In Korean phrasebooks for foreigners.
Between strangers, especially those older or of equal age.
Between female co-workers or friends.

Haera-che(Formality: high, Politeness :low) is generally called the "plain" style. It is used:
To close friends or relatives of similar age, and by adults to children.
In impersonal writing (books, newspapers, and magazines) and indirect quotations ("She said that...").
In grammar books, to give examples.

For example 
with 여자이다,
나는 여자이다 is Haera-che
저는 여자에요 is Haeyo-che
저는 여자입니다 is Hasipsio-che

with 작다
집이 작다 is Haera-che
집이 작아요 is Haeyo-che
집이 작습니다 is Hasipsio-che

Refer to https://en.wikipedia.org/wiki/Korean_speech_levels

with 귀엽다
강아지가 귀엽다 is Haera-che
강아지가 귀여워요 is Haeyo-che
강아지가 귀엽습니다 is Hasipsio-che
강아지가 귀여워 is Hae-che

First of all 강아지 means "puppy" not "dog". "Dog" is 개. I guess if you are describing a particular puppy, that 강아지가 would be best. 
Though even now, I'm not entirely 100% sure when to use 가 and 는 (though I often have a gut feeling about it).

The verb conjugation is wrong. A lot of verbs ending in ㅂ may drop the ㅂ and add 우/워 instead.

강아지가 귀엽입니다

강아지가 귀여워요 

강아지가 귀여워