I am traveling from Chiang Mai to Bangkok via train with my dog and will arrive at the train station early in the morning, about 7am.

Do you think I will have a problem getting a taxi to Pattaya from there? How much should I expect to pay?

I am concerned that I will get stuck at the train station with my dog in tow.

Can't imagine you would have any problem getting a taxi at any time of day from Hualamphong station. Even if not every taxi driver wanted to make the journey to Pattaya, there are enough taxis milling about that somebody will want to go. Don't know anything about what the fare would potentially be.

Warning: lots of touts that will try to leech onto you outside Hualamphong. You may want to consider getting off the train at Don Muang station and catch a taxi from the old airport. This would save you the bother having to leave town in morning traffic. I wouldn't think the distance is all that much greater from Don Muang than from Hualamphong.

There is an early morning train to Pattaya from Bangkok

Thanks ovenman and my friend I. I appreciate your suggestions.

There is an early morning train to Pattaya from Bangkok

I had thought of that but the connecting train is probably too early. That train departs Hualamphong at 06:55.